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The molecular graph theory is one of the essential tools for developing and constructing molecular structure. In particular, using topological invariant, which is a numerical descriptor of molecular graph, has become widespread in predicting physical properties. Topological indices provide knowledge about the overall form of molecular graphs, particularly various degree-based topological indices. This research paper focuses on the first and second Zagreb index and their coindices for the line graph of a transition metal-organic network. The network, denoted by L (TM − TCNB) , comprises the transition metals Ti, V, Cr, Fe, Co, Ni, Cu or Zn, and the TCNB ligand. The line graph of a network is a graph that represents the connections between the edges of the original network. The Zagreb indices are widely used to describe the molecular graph's shape and structure. The paper highlights the importance of these indices in modelling the chemical properties of the transition metal-organic network. The study results show that the Zagreb indices and their coindices strongly correlate with several physical characteristics, for instance the boiling points, melting points, and density of the network. [ABSTRACT FROM AUTHOR]

L-valine is considered one of the essential amino acids for mammals, which belongs to the glycogen types of amino acids. This amino acid is valuable for making protein. Due to the diverse structure of N-salicylidene-L-valine and its higher catalytic and cytotoxic activity it gains impressive interest. To study this structure more deeply and to know more about its properties in terms of topological indices, we study the supramolecular chain in dialkyltin of complex- 2 , 3 , and 4 of N-salicylidene-L-valine. In the end, we provide a comparative study of these structures by taking particular examples and also gives a comparison between topological indices. [ABSTRACT FROM AUTHOR]

Due to the recent economic crisis of the world, producing low-cost objects in every field of science and engineering is the main topic of research. Making small in-sized objects, low in budget and weight, and efficient in quality is necessary for the present and future world. In this whole scenario, nanotechnology contributing more than enough. Nanomaterials and nano-objects are highly preferable, carbon nanotubes are one of the highly chosen structures of nanomaterials, which is used in different chemical, biological, and technological fields. This thought leads us to study its different aspects of physical and chemical properties. Topological descriptors are used to characterize different molecular structures by making its numerical quantitative analysis. This article deals with different carbon nanotube structures, studying their chemical and physical characterizations and comparing armchair, semicapped, and capped carbon nanotubes. It provides the best option by making comparative analysis with different tools and algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the degree based topological properties of the novel planar metal-organic networks TM – TCNB. Interestingly, the TM – TCNB systems are metallic in any event in one turn heading and show long-run ferromagnetic coupling on the off chance that for attractive structures, which speak to perfect applicants and a fascinating possibility of uncommon applications in spintronics. Chemical graph theory plays an important role in modeling and designing any chemical structure. The topological indices are the numerical invariants of a molecular graph and are very useful for predicting their physical properties. We have computed the degree based topological indices for this metal-organic networks TM – TCNB. [ABSTRACT FROM AUTHOR]

A carbon nanotube is made up of a molecular structure of a regular hexagonal lattice. This tube can be extended by closing one- or both end of the tube, denoted by semi-capped and capped nanotube. Due to its different structures, it is categorized into three forms, despite every form or shape, it has a wide range of usage. As a memory device, current-carrying device, regenerative study of medicines, and highly recommended in tissue engineering. Due to its numerous applications, there is immense interest to study its physical and chemical properties. As nanotube and its shape is motivated by a molecular structure and topological descriptors are also tools to study different molecular structures, we use this tool to analyze different nanotube structures like armchair carbon, semi-capped, and capped nanotube by Zagreb indices and its co-indices. Moreover, we also compared capped (semi or full) and uncapped armchair carbon nanotube and provided sufficient results of the comparison. [ABSTRACT FROM AUTHOR]

In the study of QSAR/QSPR, topological indices such as Shultz index, generalized Randic index, Zagreb index, general sum-connectivity index, atom-bond connectivity (ABC) index and geometric–arithmetic (GA) index are exploited to estimate the bioactivity of chemical compounds. A topological index attaches a chemical structure with a numeric number. There are numerous applications of graph theory in this field of research. In this paper we computed generalized Randic, general Zagreb, general sum-connectivity, ABC, GA, ABC 4 and GA 5 indices of the line graphs of 2 D -lattice, nanotube and nanotorus of TUC 4 C 8 [ p, q ] by using the concept of subdivision. [ABSTRACT FROM AUTHOR]

In this work, we study the degree-based topological invariants, and the general sum-connectivity, A B C 4 , G A 5 , general Zagreb, G A , generalized Randić, and A B C indices of the line graphs of some rooted product graphs ( C n { P k } and C n { S m + 1 } ) are determined by menas of the concept of subdivision. Moreover, we also computed all these indices of the line graphs of the subdivision graphs of i-th vertex rooted product graph C i , r { P k + 1 } . [ABSTRACT FROM AUTHOR]