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This work is devoted to establish a general expression for calculating the bond incident degree (BID) indices of polyomino chains and to characterize the extremal polyomino chains with respect to several well known BID indices. From the derived results, all the results of the papers (An and Xiong, 2016, Deng et al., 2014, Yarahmadi et al., 2012) and some results of the papers (Rada, 2014, Ali et al., 2015) are obtained as corollaries. [ABSTRACT FROM AUTHOR]

This paper presents two conformance indexes that can be used to measure a similarity between two delineated structures. The authors use the presented conformance indexes for rating the results of Poisson Surface Reconstruction algorithm on real patient datasets. The rating is based on three delineations: original contours created during a standard procedure, reconstructed contours and reference contours created with an extra care by another physician. The chosen conformance indexes compare the delineations in two different forms: as a voxel grid and as a surface mesh. In this paper each of the conformance indexes is calculated in three different modes: the standard mode where all differences between datasets are taken into account and two more measuring how much one dataset exceeds the other. The last two modes are not symmetrical. The proposed conformance indexes allowed us to compare efficiently two delineations. The presented results also allow to state that the use of mesh reconstruction algorithms can improve delineations prepared within a limited time frame. [ABSTRACT FROM AUTHOR]

Sierpi n ´ ski-like graphs constitute an extensively studied family of graphs of fractal nature applicable in topology, mathematics of the Tower of Hanoi, computer science, and elsewhere. In this paper, some indexes related to degree of the Sierpi n ´ ski-like graphs have been researched. Using special structure and correlation of Sierpi n ´ ski-like graphs, the radii, Randi c ´ index, Zagreb index, sum-connectivity index and metric dimension of some Sierpi n ´ ski-like graphs are obtained. [ABSTRACT FROM AUTHOR]

In this paper we disprove three conjectures from Dehmer et al. (2014) on graph distance measures based on topological indices by providing explicit classes of trees that do not satisfy proposed inequalities. The constructions are based on the families of trees that have the same Wiener index, graph energy or Randić index – but different degree sequences. [ABSTRACT FROM AUTHOR]

The Graovac–Ghorbani index ( ABC GG ), was introduced by Graovac and Ghorbani, (2010). In this paper we present some upper and lower bounds on the ABC GG index and characterize the extremal graphs. [ABSTRACT FROM AUTHOR]

Mili c ˘ evi c ´ et al. first introduced the reformulated Zagreb indices, which is a generalization of classical Zagreb indices of chemical graph theory. As we know, the Zagreb indices have been found applications in QSPR and QSAR studies. In the paper, we characterize the extremal properties of the first reformulated Zagreb index. We show some graph operations which increase or decrease this index. Furthermore, we determine the sharp bound of the first reformulated Zagreb index among all the extremal tricyclic graphs by these graph operations. [ABSTRACT FROM AUTHOR]

For a given graph G , the well-known Randić index of G , introduced by Milan Randić in 1975, is defined as R ( G ) = ∑ u v ∈ E ( G ) ( d u d v ) − 1 / 2 , where the sum is taken over all edges uv and d u denotes the degrees of u . Bollobás and Erdös generalized this index by replacing − 1 / 2 with any real number α , which is called the general Randić index. Dvořák et al. introduced a modified version of Randić index: R ′ ( G ) = ∑ u v ∈ E ( G ) ( max { d u , d v } ) − 1 . Based on this, recently, Knor et al. introduced two generalizations: R α ′ ( G ) = ∑ u v ∈ E ( G ) min { d u α , d v α } and R α ′ ′ ( G ) = ∑ u v ∈ E ( G ) max { d u α , d v α } , for any real number α . Clearly, the former is a lower bound for the general Randić index, and the latter is its upper bound. Knor et al. studied extremal values of R α ′ ( G ) and R α ′ ′ ( G ) and concluded some open problems. In this paper, we consider the open problems and give some comments and results. Some results for chemical trees are obtained. [ABSTRACT FROM AUTHOR]