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Wang and Yu (2022) prove an enhanced version of the Erdős–Lovász Tihany conjecture for line graphs of multigraphs. That is, let s , t and ℓ be arbitrary integers with t ≥ s ≥ 3. 5 ℓ + 2 , ℓ ≥ 0. If the line graph L (G) of some multigraph G has chromatic number s + t − 1 > ω (L (G)) , then there is a partition (S , T) of the vertex set V (L (G)) such that χ (L (G) [ S ]) ≥ s and χ (L (G) [ T ]) ≥ t + ℓ. In this paper, for integers s and t with t ≥ s ≥ 7 , we prove that for each line graph L (G) with χ (L (G)) = s + t − 1 ≥ ω (L (G)) , there is a partition (S , T) of the vertex set V (L (G)) such that χ (L (G) [ S ]) ≥ s and χ (L (G) [ T ]) ≥ t + 2 , which slightly improves the recent result of Wang and Yu (2022) for ℓ = 2. [ABSTRACT FROM AUTHOR]

Let G be a simple graph of order n. For $ \alpha \in [0,1] $ α ∈ [ 0 , 1 ] , the $ A_{\alpha } $ A α -matrix of G is defined as $ A_{\alpha }(G)=\alpha D(G)+ (1-\alpha)A(G) $ A α (G) = α D (G) + (1 − α) A (G) , where $ A(G) $ A (G) and $ D(G) $ D (G) are the adjacency matrix and the diagonal degree matrix of G, respectively. The eigenvalues of the $ A_{\alpha } $ A α -matrix of G are called the $ A_{\alpha } $ A α -eigenvalues of G. In this paper, we first study the properties on $ A_{\alpha } $ A α -eigenvalues, i.e. how the $ A_{\alpha } $ A α -eigenvalues behave under some kinds of graph transformations including vertex deletion, vertex contraction, edge deletion and edge subdivision. Moreover, we also present the relationships between the $ A_{\alpha } $ A α -eigenvalues of G and its k-domination number, independence number, chromatic number and circumference, respectively. [ABSTRACT FROM AUTHOR]

For a simple graph G and α ∈ [ 0 , 1 ] , Nikiforov (2017) defined the A α (G) -matrix of G as A α = α D (G) + (1 − α) A (G) , where A (G) and D (G) are the adjacency matrix and the diagonal degree matrix of G , respectively. The A α -spectral radius of G , denoted by ρ α (G) , is the largest eigenvalue of A α (G). Wang and Guo (2022) proved that for an integer k ≥ 0 and a graph G of size m , if ρ 1 2 (G) ≥ 1 2 (m − k + 1) , then K 1 , m − k ⊆ G. In this paper, we extend their result to A α -spectral radius for α ∈ [ 1 2 , 1). Moreover, for α ∈ [ 1 2 , 1) , we also determine the graph with maximum A α -spectral radius among graphs of given size and girth, which generalizes the result of Chen, Wang and Zhai (2022) for α = 1 2 . [ABSTRACT FROM AUTHOR]

Let λ 1 (Σ) be the largest eigenvalue of a signed graph Σ . Wang–Yan–Qian (Linear Algebra Appl 619:137–145, 2021) and Kannan–Pragada (Linear Algebra Appl 663:62–79, 2023) extended the spectral bounds of Wilf and Nikiforov for the balanced clique number of signed graphs and derived upper bounds on λ 1 (Σ) in terms of its balanced clique number. In this paper, we characterize the extremal signed graphs attaining these upper bounds. Moreover, a relationship between λ 1 (Σ) and λ 1 (Σ - v) for some v ∈ V (Σ) is included. [ABSTRACT FROM AUTHOR]

An edge labeling of a connected graph G = (V , E) is said to be local antimagic if it is a bijection f : E → { 1 , ... , | E | } such that for any pair of adjacent vertices x and y, f + (x) ≠ f + (y) , where the induced vertex label f + (x) = ∑ f (e) , with e ranging over all the edges incident to x. The local antimagic chromatic number of G, denoted by χ la (G) , is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. In this paper, we show the existence of infinitely many bipartite and tripartite graphs with χ l a = 2 , 3. [ABSTRACT FROM AUTHOR]

A subset S of vertex set V(G) of a graph G is a zero forcing set of G if iteratively adding vertices to S from V (G) \ S that are the unique neighbor in V (G) \ S of some vertex in S, results in the entire V(G) of G. Additionally, if the subgraph induced by S is connected, then S is a connected forcing set of G. The zero (resp., connected) forcing number, denoted by F(G) (resp., F c (G) ), of G is the minimum cardinality of a zero (resp., connected) forcing set of G. Davila and Kenter [Theory Appl. Graphs, 2(2) (2015) Article 1] proved that F (G) ≤ n - g + 2 for graphs G of finite girth g and order n (≥ g) . In this paper, first, we restrict G to be connected and improve the upper bound according to the value of g: F (G) ≤ n - g + 2 when g = 3 , 4 or n; F (G) ≤ n - g + 1 when g = 5 , 6 or n - 1 (n ≥ 6) and F (G) ≤ n - g when 7 ≤ g ≤ n - 2 . Further, the extremal graphs are characterized, respectively. Davila et al. [Graphs Combin. 34 (2018) 1159-1174] proved a similar upper bound on F c (G) for 2-connected graphs G with n vertices and finite girth g: F c (G) ≤ n - g + 2 . Secondly, we prove that F c (G) = n - g + 2 if and only if G is C n , or K n , or K a , b for integers a , b ≥ 2 , a + b = n . Finally, we also characterize all connected triangle-free or subcubic graphs G of order n with F (G) = n - 3 . [ABSTRACT FROM AUTHOR]

An edge labeling of a connected (p, q) -graph G = (V, E) of order p and size q is a modulo local antimagic labeling if it is a bijection π : E → {1, ... ,q} such that for any pair of adjacent vertices u and v, π+(u) ≠ π+(v), where the induced vertex label π+(u) = ∑π(e)(mod p), with e ranging over all the edges incident to u. The modulo local antimagic chromatic number of G, denoted πla(G), is the minimum number of distinct induced vertex labels over all modulo local antimagic labelings of G. In this paper, we shall study the relationship among chromatic number, local antimagic chromatic number and modulo local antimagic chromatic number of graphs. Many open problems for further research are also presented. [ABSTRACT FROM AUTHOR]

Using the eigenvalues of a graph to reflect its structural properties is a central topic in spectral graph theory. Especially, the relationships between the eigenvalues of a graph and its structural parameters have been studied extensively. In this paper, we explore the relationships between the (normalized) Laplacian eigenvalues of a graph and its ℓ -connectivity, integrity, tenacity and toughness. Some of our results extend or improve the related existing results. [ABSTRACT FROM AUTHOR]

Let G be a graph with adjacency matrix A (G) and D (G) be the diagonal matrix of the degrees of G. Nikiforov (2017) defined the matrix A α (G) as A α (G) = α D (G) + (1 − α) A (G) , α ∈ [ 0 , 1 ]. The A α -spectral radius is the largest eigenvalue of A α (G). Let G m d be the set of all connected graphs with size m and diameter d. In this paper, we determine the graphs with maximal A α -spectral radius among all graphs in G m d. [ABSTRACT FROM AUTHOR]

DP-coloring as a generalization of list coloring was introduced recently by Dvořák and Postle. The D P -chromatic number of G , denoted by χ D P (G) , is the minimum number k such that G is D P − k -colorable. The variation of the Randić index R ′ (G) of a graph G is defined as the sum of the weights 1 m a x { d (u) , d (v) } of all edges u v of G , where d (u) is the degree of the vertex u in G. In this paper, we show that for any graph G of order n , χ D P (G) ≤ 2 R ′ (G) , and this bound is sharp for all n and 2 ≤ χ D P (G) ≤ n. [ABSTRACT FROM AUTHOR]

A strong edge-coloring of a graph G is a proper edge coloring such that every path of length 3 uses three different colors. The strong chromatic index of G, denoted by χ s ′ (G) , is the least possible number of colors in a strong edge-coloring of G. In this paper, we prove that if G is a claw-free subcubic graph other than the prism graph, then χ s ′ (G) ≤ 8 . [ABSTRACT FROM AUTHOR]

For a simple graph G , let n (G) , η (G) , r (G) and g (G) be respectively the order, the nullity, the rank and the girth of G. It was shown by Cheng and Liu (2007) that for every graph G , η (G) ≤ { n (G) − g (G) + 2 if 4 | g (G) n (G) − g (G) if 4 ∤ g (G) . Connected graphs G with η (G) = n (G) − g (G) + 2 and n (G) − g (G) respectively have been characterized by Zhou et al. (2021). In this paper, we characterize connected graphs G with η (G) = n (G) − g (G) − 1. [ABSTRACT FROM AUTHOR]

A cast brass ewer was unearthed from the Shangfang Śarīra Stupa crypt at Qingshan Monastery. Most likely, it was made in the northwestern part of the South Asian subcontinent in the late seventh century. Integrating ancient Roman, Sassanian, and early Islamic styles, the shape of this ewer not only is a mixture of the elements of different eras and traditions but also reflects unique attributes. The multi-headed and multi-armed deities from Hinduism, especially Skanda, may have inspired the six-faced design on the body. Eventually, the ewer was taken to Chang'an by Indian or Kashmirian monks and buried in the pagoda's crypt. [ABSTRACT FROM AUTHOR]

An edge-coloring of a graph G is injective if for any two distinct edges e 1 and e 2 , the colors of e 1 and e 2 are distinct if they are at distance 2 in G or in a common triangle. The injective chromatic index of G , χ i n j ′ (G) , is the minimum number of colors needed for an injective edge-coloring of G. In this paper, we consider the list version of the injective edge-coloring and prove that the list-injective chromatic index of every subcubic graph is at most 7, which generalizes the recent result of Kostochka et al. (2021). [ABSTRACT FROM AUTHOR]

Let G n , k D be the set of all k -connected graphs of order n with diameter D. In this paper, we determine the graphs with maximal signless Laplacian spectral radius among all graphs in G n , k D. [ABSTRACT FROM AUTHOR]

• The highly flame-retardant EVA-ATH-MCA composites were prepared. • ATH and MCA played as a synergetic fire retardant for EVA composites. • MCA addition increased the compatibility and thermal stability of the EVA composites. • The EVA-60-40 possessed a rather high LOI value of 27.5% and flame resistance. There is a great interest to develop efficient fire-resistant materials. While ethylene vinyl acetate (EVA) is a widely used material, it suffers from the problem of relatively high inflammability which seriously hinders its usage as the product material with a high flame-retardant requirement. In this study, a strategy to combine aluminum hydroxide (ATH) and melamine cyanurate (MCA) with EVA was proposed to prepare the EVA composite materials with high flame resistance. It was found that slight addition of MCA could increase the lubricity of EVA and raise the compatibility between EVA and ATH. Thermogravimetric analysis (TGA) indicated that the thermal stability of EVA was improved via adding MCA, which was evidenced by the delayed thermal decomposition temperature. Moreover, the combustion results indicated that the EVA composite with 60 parts per hundred (phr) ATH and 40 phr MCA addition (EVA-60-40) displayed the optimal isolated layer favoring the fire resistance. In addition, the highest limiting oxygen index (LOI) value (27.5%) and V-0 rating of the EVA-60-40 as compared with other components indicated its incombustible nature. These results suggested the synergetic effect of ATH and MCA additions, the high efficiency of the proposed strategy and the wide application prospect of the produced EVA-ATH-MCA composite materials. [ABSTRACT FROM AUTHOR]

The harmonic index H (G) of a graph G is defined as the sum of the weights 2 d (u) + d (v) of all edges u v of G , where d (u) is the degree of the vertex u in G. The D P -chromatic number of G , denoted by χ D P (G) , is the minimum number k such that G is D P - k -colorable. In this paper, we show that χ D P (G) ≤ 2 H (G) , and the equality holds if and only if G is a complete graph possibly with some additional isolated vertices. This generalizes the result of Deng et al. (2013) and Wu et al. (2017), respectively. [ABSTRACT FROM AUTHOR]

An edge-coloring of a graph G is injective if for any two distinct edges e 1 and e 2 , the colors of e 1 and e 2 are distinct if they are at distance 2 in G or in a common triangle. The injective chromatic index of G, χ inj ′ (G) , is the minimum number of colors needed for an injective edge-coloring of G. In this note, we show that every K 4 -minor free graph G with maximum degree Δ (G) ≥ 3 satisfies χ inj ′ (G) ≤ 2 Δ (G) + 1 . [ABSTRACT FROM AUTHOR]

In this study, LDPE materials with different kinds of antioxidants were prepared by melt-blending method. To reveal the aging mechanism and the anti-oxidation efficiency of LDPE in the presence of copper, series of characterizations including tensile testing, Fourier transform infrared spectra (FTIR), differential scanning calorimetry (DSC), scanning electronic microscopy (SEM) and computation simulation were performed. The experimental results indicated that the aging process significantly decreased the tensile strength and elongation of those aged samples except 1024, which retarded the aging degradation of LDPE at the same condition. These results were further confirmed by the FTIR analysis with the carbonyl index values. Additionally, the melting peaks of DSC plots became broader and shifted to the lower temperatures during the aging process for S-0, S-3114 and S-1010, whereas no obvious changes were observed for S-1024. Importantly, according to the results obtained from computation simulation, a strong metal-ligand interaction between hydrazide group and copper ions was formed to prevent the further oxidation, which accounted for the excellent anti-oxidation behavior of 1024 for LDPE in the presence of copper. [ABSTRACT FROM AUTHOR]

In this study, two types of amine‐containing antioxidants composed of 2‐mercaptobenzimidazole zinc (MBZ) and 4,4′‐bis(α, α‐dimethylbenzyl) diphenylamine (445) were used to improve the thermo‐oxidative aging resistance of ethylene propylene diene rubber (EPDM). The synergistic effects on the performances of EPDM and the corresponding aging mechanism were investigated by FTIR, tensile test, differential scanning calorimetry (DSC), rotary rheometer and other equipment. The results showed that the hardness increased gradually with the increasing aging time regardless of the type of antioxidants. Compared with the EPDM without antioxidants, the elongation retention of those samples with MBZ or 445 improved obviously. Additionally, the sample with the MBZ/445 complex showed the highest retention values at the same aging time. The antioxidative mechanisms were further analyzed by carbonyl index, activation energy and oxidation induction time, respectively. Results indicated that the degree of oxidation of EPDM using the MBZ/445 complex was much lower than other control systems during the aging process. As a result, the MBZ/445 complex was a favorable antioxidative additive for EPDM. [ABSTRACT FROM AUTHOR]

Let G be a simple connected graph of order n . Its normalized Laplacian eigenvalues are λ 1 ≥ λ 2 ≥ ⋯ ≥ λ n − 1 ≥ λ n = 0 . In this paper, new bounds on S β * ( G ) = ∑ i = 1 n − 1 λ i β ( β  ≠ 0, 1) are derived. [ABSTRACT FROM AUTHOR]

In this study, a new strategy which blends low-density polyethylene (LDPE), magnesium hydroxide (MH) and lauryl acrylate by electron-beam radiation for production of LDPE-based composites with high performance was proposed. It was found that, MH played main roles in flame retardancy but reduced processing flow and mechanical properties of the composites. Meanwhile, melt flow rate (MFR) increased while viscosity of the composites decreased with lauryl acrylate content increased, facilitating LDPE composites processing. Electron beam radiation could prompt crosslinking of lauryl acrylate, which significantly enhanced the mechanical properties of LDPE composites. Meanwhile, lauryl acrylate addition only slightly decreased the flame retardancy, suggesting that LDPE composites could remain high flame retardancy even when lauryl acrylate content was high. The study highly demonstrated the feasibility to produce LDPE-based composites simultaneously with high flame retardancy and high mechanical properties by the blending strategy provided in this study. [ABSTRACT FROM AUTHOR]

The phenoxycyclophosphazene (HPCTP), as a coupling reagent, was introduced into ultra-high-molecular-weight polyethylene (UHMWPE)-magnesium hydroxide (MH) composites to overcome the incompatibility problem. The Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), and scanning electron microscopy (SEM) results confirmed that HPCTP had successfully been introduced into the UHMWPE-MH composites and performed as a coupling reagent. The prepared UHMWPE-MH-HPCTP composites performed promotion of processability, which is indicated by the over 100% increasing of melt flow rate (MFR). The elongation of composites was promoted nearly 600% under the optimized composition of UHMWPE-MH-HPCTP. Although the thermal property was slightly affected, the UHMWPE-MH-HPCTP composites presented significantly enhanced flame retarding ability, which was sufficiently confirmed by 100% promotion of limiting-oxygen index (LOI), 75 s delaying of ignition time and advantageous ash results. By addition of HPCTP, the prepared UHMWPE-MH-HPCTP composites expressed priorities in processability, mechanical property, especially flame retarding ability, and supplied a practical candidate material for the industrial applications. [ABSTRACT FROM AUTHOR]

In this paper, we give a combinatorial expression for the fifth coefficient of the (signless) Laplacian characteristic polynomial of a graph. The first five normalized Laplacian coefficients are also given. [ABSTRACT FROM AUTHOR]

Crystal modifier is an important factor in preparation of α-hemihydrate gypsum (α-CaSO 4 ·0.5H 2 O) from phosphogypsum (PG). Here, α-CaSO 4 ·0.5H 2 O was prepared from PG using a semi-dry method. SEM, XRD, XPS were used to explore the effects of one or more crystal modifiers on crystal growth and mechanical properties after hydration and hardening of α-CaSO 4 ·0.5H 2 O. The results showed that addition of RCOO − can delay the hydration process of α-CaSO 4 ·0.5H 2 O and improve productivity. Al 3+ can be adsorbed selectively on the gypsum crystal surface, inhibiting the crystal growth along axis c, which could alter the speed in all directions and turn the crystal into a short hexahedron pole. But when RCOO − and Al 3+ were composited, a superposition effect occurred, resulting in production of a crystal with a smaller length to diameter ratio and more perfect crystal form. When RCOO − and Al 3+ were both added in 0.06% level, the flexural and compressive strength of the hardened α-CaSO 4 ·0.5H 2 O could reach to 6.7 and 25.65 MPa, respectively. [ABSTRACT FROM AUTHOR]

The normalized Laplacian eigenvalues of a network play an important role in its structural and dynamical aspects associated with the network. In this paper, we consider how the normalized Laplacian spectral radius of a non-bipartite graph behaves by several graph operations. As an example of the application, the smallest normalized Laplacian spectral radius of non-bipartite unicyclic graphs with fixed order is determined. [ABSTRACT FROM PUBLISHER]

In this paper, we firstly consider how the normalized Laplacian spectral radius of a non-bipartite graph behaves by several graph operations. As applications of the result, the largest normalized Laplacian spectral radius of non-bipartite unicyclic graphs with fixed order and girth is determined. Moreover, the largest normalized Laplacian spectral radius among non-bipartite unicyclic graphs with fixed girth and order is also determined. The maximizer is the tadpole graph with the same (odd) girth. [ABSTRACT FROM AUTHOR]

The harmonic index of a graph G is defined as the sum of weights $$\frac{2}{d(u)+d(v)}$$ over all edges uv of G, where d( u) and d( v) are the degrees of the vertices u and v in G, respectively. Let $$\mathscr {T}(n,\gamma )$$ and $$\mathscr {C}_n^\pi $$ be the sets of trees of order n with domination number $$\gamma $$ and connected graphs of order n with degree sequence $$\pi $$ , respectively. In this paper, the tree with minimum harmonic index among trees in $$\mathscr {T}(n,\gamma )$$ is determined, as well as the trees with maximum harmonic index among trees in $$\mathscr {T}(n,\gamma )$$ when $$\gamma =2,\lceil \frac{n}{3}\rceil $$ . Moreover, we show that among graphs in $$\mathscr {C}_n^\pi $$ , the maximum harmonic index is attained by a BFS graph. [ABSTRACT FROM AUTHOR]

Abstract: Let be the second smallest normalized Laplacian eigenvalue of a graph . In this paper, we investigate the behavior on when the graph is perturbed by separating an edge. This result can be used to determine all trees and unicyclic graphs with . Moreover, the trees and unicyclic graphs with are also determined, respectively. [Copyright &y& Elsevier]

Abstract: The normalized algebraic connectivity of a graph G, denoted by , is the second smallest eigenvalue of its normalized Laplacian matrix. In this paper, we firstly determine all trees with . Then we classify such trees into six classes and prove that for , where and . At the same time, the values of the normalized algebraic connectivity for the six classes of trees are provided, respectively. These results are similar to those on the algebraic connectivity which were obtained by Yuan et al. (2008) [8]. [Copyright &y& Elsevier]

Abstract: Retained placenta remains therapeutic challenge in cattle. Certain traditional medicines are believed to be able to alleviate retained placenta condition and improve overall fertility in cows. The aim of the present study was to evaluate the efficacy of an herbal tincture for treatment of retained placenta. The herbal tincture was extracted from a combination of Herba Leonuri, Angelicae Sinensis Radix, Flos Carthami, Myrrha and Rhizoma Cyperi by percolation with 70% ethanol to a concentration of 0.5g crude herb/ml. Cows diagnosed with retained placenta (n =48) were randomly divided into one of two treatment groups (A and B), with animals in group A (n =26) receiving herbal tincture orally, and cows in group B (n =22) receiving oxytetracycline infusion into the uterus. Eighty six cows with no clinically visible pathological conditions, given birth alone and with no retained placenta diagnosis were included into control group (C). Retained placenta was expelled within 72h following initial treatment in 19 cows in group A, yet no cows in group B were recorded to expel placenta in the same time. The median number of days to first service (70.0 vs. 102.5 days; P <0.05) and median number of days open (76.0 vs. 134.0 days; P <0.01) were lower in group A than in group B. Percentage of cows pregnant within 100 days postpartum was the highest for animals in group A compared to controls (61.5% vs. 39.5%, P <0.05), and for animals in group B (61.5% vs. 22.7%; P <0.01). Herbal tincture used in the present study might facilitate expulsion of retained placenta and improve subsequent fertility, thus could present effective treatment option for retained placenta in cows. [Copyright &y& Elsevier]

Abstract: Let G be a simple graph with n vertices, m edges. If each edge of G belongs to t triangles ( ), then we present a new upper bound for the Laplacian spectral radius of G which improves some known upper bounds. [Copyright &y& Elsevier]

Abstract: The second largest Laplacian eigenvalue of a graph is the second largest eigenvalue of the associated Laplacian matrix. In this paper, we study extremal graphs for the extremal values of the second largest Laplacian eigenvalue and the Laplacian separator of a connected graph, respectively. All simple connected graphs with second largest Laplacian eigenvalue at most 3 are characterized. It is also shown that graphs with second largest Laplacian eigenvalue at most 3 are determined by their Laplacian spectrum. Moreover, the graphs with maximum and the second maximum Laplacian separators among all connected graphs are determined. [Copyright &y& Elsevier]

Abstract: The Laplacian spectral radius of a graph G is the largest eigenvalue of its Laplacian matrix. In this paper, the first three smallest values of the Laplacian spectral radii among all connected graphs with clique number are obtained. [Copyright &y& Elsevier]

Abstract: The Hosoya index and the Merrifield–Simmons index of a graph are defined as the total number of the matchings (including the empty edge set) and the total number of the independent vertex sets (including the empty vertex set) of the graph, respectively. Let be the set of connected -vertex graphs with connectivity at most . In this note, we characterize the extremal (maximal and minimal) graphs from with respect to the Hosoya index and the Merrifield–Simmons index, respectively. [Copyright &y& Elsevier]

Abstract: The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we provide structural and behavioral details of graphs with maximum Laplacian spectral radius among all bipartite connected graphs of given order and size. Using these results, we provide a unified approach to determine the graphs with maximum Laplacian spectral radii among all trees, and all bipartite unicyclic, bicyclic, tricyclic and quasi-tree graphs, respectively. [Copyright &y& Elsevier]

Abstract: The algebraic connectivity of is the second smallest eigenvalue of its Laplacian matrix. Let be the set of all unicyclic graphs of order . In this paper, we will provide the ordering of unicyclic graphs in up to the last seven graphs according to their algebraic connectivities when . This extends the results of Liu and Liu [Y. Liu, Y. Liu, The ordering of unicyclic graphs with the smallest algebraic connectivity, Discrete Math. 309 (2009) 4315–4325] and Guo [J.-M. Guo, A conjecture on the algebraic connectivity of connected graphs with fixed girth, Discrete Math. 308 (2008) 5702–5711]. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present some sharp upper bounds for the number of spanning trees of a connected graph in terms of its structural parameters such as the number of vertices, the number of edges, maximum vertex degree, minimum vertex degree, connectivity and chromatic number. [Copyright &y& Elsevier]

Abstract: Let be the set of all trees of order with perfect matchings. In this paper, we prove that for any tree , its th largest Laplacian eigenvalue satisfies when , and when . Moreover, this upper bound is sharp when . [Copyright &y& Elsevier]

Abstract: The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we determine those graphs which maximize the Laplacian spectral radius among all bipartite graphs with (edge-)connectivity at most . We also characterize graphs of order with cut-edges, having Laplacian spectral radius equal to . [Copyright &y& Elsevier]

Abstract: In this paper, we provide the smallest value of the second largest Laplacian eigenvalue for any unicyclic graph, and find the unicyclic graphs attaining that value. And also give an “asymptotically good” upper bounds for the second largest Laplacian eigenvalues of unicyclic graphs. Using this results, we can determine unicyclic graphs with maximum Laplacian separator. And unicyclic graphs with maximum Laplacian spread will also be determined. [Copyright &y& Elsevier]

Simple Summary: Astragali Radix cell wall is composed of dense components, which greatly reduces the utilization rate of its active constituents and limits its application and promotion in animals. The application of microbial fermentation technology can effectively address this issue. We produced a mixed-bacterial-fermented Astragalus powder. In this study, we found that fermented Astragalus powder has the potential to enhance the growth performance, immune function, and antioxidant capacity of broilers to a certain degree. Additionally, it has shown promising effects in regulating the intestinal flora. Fermented Astragalus powder is expected to be a novel kind of feed additive. A total of 320 1-day-old broilers were randomly divided into five groups. The control group (CON) received a basal diet, while the FAP4, FAP2, and FAP1 groups were provided with the basal diet supplemented with 4%, 2%, and 1% fermented Astragalus powder, respectively. The unfermented Astragalus powder (UAP2) group was fed the basal diet supplemented with 2% UAP. Each group contained eight replicates of eight chicks each. The results revealed that the final BW and ADG in the FAP 1 and FAP2 were higher than those in the UAP2 and CON groups, while reducing F/G from day 14 to day 42. On day 42, the thymus index in the UAP and FAP groups as well as the bursa index in the FAP4 group showed significant increases compared to those in the CON group. Supplementation with 2% FAP elevated serum IgA levels in broilers on day 28 and day 42, and it also increased serum IgG levels on day 42. Furthermore, supplementation with 2% FAP elevated serum albumin (ALB) levels in broilers, while supplementation with 4% FAP increased serum (glucose) GLU levels in broilers on day 28. The serum biochemical parameters and pathological observation of the liver and kidney in the groups did not show any adverse effects on broilers' health. In addition, the serum total antioxidant capacity (T-AOC) level significantly increased in the FAP4 and FAP2 groups on day 28, and the malondialdehyde (MDA) level in both serum and liver tissue decreased in the FAP2 group on day 28 and day 42. Compared to the CON group, 2% FAP and 2% UAP supplementation reduced the relative abundance of Bacteroides and supplementation with 2% FAP increased the relative abundance of Alistipes on day 42. In conclusion, the dietary supplementation of FAP can enhance the growth performance, immune function, and antioxidant capacity and regulate microflora in broilers, of which 2% FAP is more effective. It indicates FAP exhibits significant application potential as a promising feed additive for broilers. [ABSTRACT FROM AUTHOR]

This study investigates the impact of Titanium Suboxide (Ti4O7) on the flame retardancy, mechanical properties, thermal stability, and electrical and thermal conductivity of silicone rubber composites. The addition of 1.0 part of Ti4O7 to the silicone rubber composites results in a total heat release (THR) of 45 MJ/m2, which is 45.7% lower than the silicone rubber without Ti4O7, leading to a decrease in the peak of heat release rate (PHRR). Furthermore, Ti4O7 exhibits temperature stability at low temperatures and acts as a physical barrier, inhibiting the early decomposition of silicone rubber and enhancing the thermal stability of the composites. However, at temperatures exceeding 450°C, the catalytic activity of Ti4O7 is activated, promoting the decomposition of the silicone rubber composites and generating more residue. The addition of an appropriate amount of Ti4O7 can further improve the mechanical properties of the silicone rubber composites and enhance their electrical and thermal conductivity. [ABSTRACT FROM AUTHOR]

Strain-specific probiotics can present antioxidant activity and reduce damage caused by oxidation. Streptococcus alactolyticus strain FGM (S. alactolyticus strain FGM) isolated from the chicken cecum shows potential probiotic properties which have been previously demonstrated. However, the antioxidant properties of S. alactolyticus strain FGM remain unknown. In this view, cell-free supernatant (CFS), intact cells (IC) and intracellular extracts (CFE) of strain FGM and 3 strains of Lactobacillus (LAB) were prepared, and their scavenging capacities against DPPH, hydroxyl radicals and linoleic acid peroxidation inhibitory were compared in this study. The effects of strain FGM cell-free supernatant (FCFS) on NO production, activity of SOD and GSH-Px in RAW264.7 cells and LPS-induced RAW264.7 cells were analyzed. The metabolites in the supernatant were quantitated by N300 Quantitative Metabolome. It was shown that the physicochemical characteristics of CFS to scavenge DPPH, hydroxyl radicals, and linoleic acid peroxidation inhibitory were significantly stronger than that of IC and CFE in the strain FGM (P < 0.05), respectively 87.12% ± 1.62, 45.03% ± 1.27, 15.63% ± 1.34. FCFS had a promotional effect on RAW264.7 cells, and significantly elevated SOD and GSH-Px activities in RAW264.7 cells. 25 μL FCFS significantly promoted the proliferation of RAW264.7 cells induced by LPS, increased the activities of SOD and GSH-PX, and decreased the release of NO. Furthermore, among the differential metabolites of FCFS quantified by N300, 12 metabolites were significantly up-regulated, including lactic acid, indole lactic acid, linoleic acid, pyruvic acid etc., many of which are known with antioxidant properties. In conclusion, FCFS had good antioxidant properties and activity, which can be attributed to metabolites produced from strain FGM fermentation. It was further confirmed that S. alactolyticus strain FGM and its postbiotic have potential probiotic properties and bright application prospects in livestock and poultry breeding. [ABSTRACT FROM AUTHOR]

The nullity η (G) of a (simple) graph G is the multiplicity of 0 as an eigenvalue of the adjacency matrix of G. It was shown by Ma et al. (2016) that for a connected graph G with n (G) vertices, e (G) edges and p (G) (≥ 1) pendant vertices, η (G) ≤ 2 c (G) + p (G) − 1 , where c (G) = e (G) − n (G) + θ (G) is the cyclomatic number of G , θ (G) being the number of connected components of G. In this paper connected graphs G and trees T that satisfy respectively the conditions η (G) = 2 c (G) + p (G) − 1 and η (T) = p (T) − 1 are characterized. Besides, we identify the matched and mismatched vertices in a tree T that satisfies η (T) = p (T) − 1 and characterize trees T that have a pendant vertex matched in T and satisfy η (T) = p (T) − 2. We obtain new sharp lower and upper bounds for a tree T with p (T) ≥ 3 , given in terms of p (T) and the numbers of two special kinds of internal paths in T. It is also proved that for any integer c ≥ 2 , the set of values attained by η (G) − n (G) + 2 m (G) , as G runs through all connected, leaf-free graphs G with cyclomatic number c , is { − c + 1 , − c + 2 , ... , 2 c − 3 , 2 c − 2 }. [ABSTRACT FROM AUTHOR]

The poly(ether-ether-ketone) (PEEK) insulation material used in the containment dome of nuclear power plant was aged by thermal aging method with an aging period of 14 days and accelerated aging at different temperatures. The mechanical properties, crystallization behavior and thermal properties were analyzed. The results showed that the fracture strength increased with the aging temperature before 290 ℃, and decreased after 290 ℃. The results of infrared spectra analyses showed that with the increase of aging temperature, the intensity of methyl absorption peak at 2916 cm−1 and 2849 cm−1 increased. At the early aging temperature, the carbonyl index basically did not change. As the aging temperature increased, the carbonyl index gradually increased in steps and the ratio of 1310 cm−1 and 1285 cm−1 bands declined linearly. Thermal-gravimetric test results showed that the residual weight of the material became smaller and smaller with the increase of aging temperature, and the maximum decomposition temperature of the material decreased gradually. DSC analysis showed that the melting peak temperature, crystallization peak temperature, enthalpy and crystallinity decreased. [ABSTRACT FROM AUTHOR]

In order to satisfy demands of cable insulation for nuclear power, a low-smoke, halogen-free flame retardant and better cryogenic property insulation was prepared. The effect of thermal-oxidative aging on the dielectric properties was researched in this paper. The changes of chemical structure and thermal-oxidative stability caused by aging were characterized by Fourier transform infrared spectroscopy and a differential scanning calorimeter. The results showed that, the oxidative-induced stability reduced as complex products accumulated during aging. The dielectric properties including polarity, conductivity and breakdown at different aging stages were measured. For comparison, tensile testing was performed. The parameters related to conductivity changed notably, and were comparable with the changes in mechanical properties. [ABSTRACT FROM AUTHOR]

An increasing amount of evidence indicates that Baicalin (Bai, a natural glycosyloxyflavone compound) exhibits an antiviral effect against avian viruses. However, it remains unclear if the antiviral effect of Bai against infectious bronchitis virus (IBV) is exerted indirectly by modulating respiratory tract microbiota and/or their metabolites. In this study, we investigated the protection efficacy of Bai in protecting cell cultures and broilers from IBV infection and assessed modulation of respiratory tract microbiota and metabolites during infection. Bai was administered orally to broilers by being mixed in with drinking water for seven days. Ultimately, broilers were challenged with live IBV. The results showed that Bai treatment reduced respiratory tract symptoms, improved weight gain, slowed histopathological damage, reduced virus loads and decreased pro-inflammation cytokines production. Western blot analysis demonstrated that Bai treatment significantly inhibited Toll-like receptor 7 (TLR7), myeloid differentiation factor 88 (MyD88) and nuclear factor kappa-B (NF-κB) expression both in cell culture and cells of the trachea. Bai treatment reversed respiratory tract microbiota dysbiosis, as shown by 16S rDNA sequencing in the group of broilers inoculated with IBV. Indeed, we observed a decrease in Proteobacteria abundance and an increase in Firmicutes abundance. Metabolomics results suggest that the pentose phosphate pathway, amino acid and nicotinamide metabolism are linked to the protection conferred by Bai against IBV infection. In conclusion, these results indicated that further assessment of anti-IBV strategies based on Bai would likely result in the development of antiviral molecule(s) which can be administered by being mixed with feed or water. [ABSTRACT FROM AUTHOR]

Background: The present study aimed to investigate the prevalence and molecular characterization of extended-spectrum β-lactamase (ESBL)—producing Escherichia coli (E. coli) isolated from dairy cattle with endometritis in China. The prevalence of ESBL-producing E. coli in sample was detected using ChromID ESBL agar, and genotyping of the ESBL producers was performed by PCR and DNA sequencing. Results: The results revealed that the proportion of positive pathogens tested was 69.76% (180/258) in samples obtained from cows diagnosed with clinical endometritis, with E. coli accounting for 170 out of the 180 positive samples. The infection rate of isolated E. coli was 39.14% (101/258), and co-infections with other pathogens were prevalent. Furthermore, among the 158 E. coli isolates, 50 strains were identified as ESBL producers, with TEM and CTX-M prevalence rates at 78.00% and 32.00%, respectively. Drug sensitivity experiments indicated that 50 isolates of ESBL- producing E. coli were multidrug resistance (MDR), with 48.0% of them exhibiting positive results for both the class 1 integron gene and five gene cassettes associated with resistance to trimethoprim (dfr1 and dfrA17) and aminoglycosides (aadA1, aadA5, and dfrA1), respectively. Conclusion: This investigation demonstrated a substantial prevalence and heightened level of antimicrobial resistance among ESBL-producing E. coli isolates derived from dairy cattle infected with endometritis in China. [ABSTRACT FROM AUTHOR]