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Sierpiński graphs are family of fractal nature graphs having applications in mathematics of Tower of Hanoi, topology, computer science, and many more diverse areas of science and technology. This family of graphs can be generated by taking certain number of copies of the same basic graph. A topological index is the number which shows some basic properties of the chemical structures. This article deals with degree based topological indices of uniform subdivision of the generalized Sierpiński graphs S(n,G) and Sierpiński gasket Sn . The closed formulae for the computation of different kinds of Zagreb indices, multiple Zagreb indices, reduced Zagreb indices, augmented Zagreb indices, Narumi-Katayama index, forgotten index, and Zagreb polynomials have been presented for the family of graphs.

Energy of a molecule plays an important role in physics, chemistry and biology. In mathematics, the concept of energy is used in graph theory to help other subjects such as chemistry and physics. In graph theory, nullity is the number of zeros extracted from the characteristic polynomials obtained from the adjacency matrix, and inertia represents the positive and negative eigenvalues of the adjacency matrix. Energy is the sum of the absolute eigenvalues of its adjacency matrix. In this study, the inertia, nullity and signature of the aforementioned structures have been discussed.

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. ...

There are different mathematical tools to establish a numeric correlation between a chemical structure and its properties. A topological index is such a successful tool. It represents a graph in fo...

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.

The Randic (product) connectivity index and its derivative called the sum-connectivity index are well-known topological indices and both of these descriptors correlate well among themselves and with the π-electronic energies of benzenoid hydrocarbons. The general n connectivity of a molecular graph G is defined as n χ(G)=∑ v i 1 v i 2 v i 3 ... v i n+1 (1/d i 1 d i 2 ... d i n+1 ) and the n sum connectivity of a molecular graph G is defined as n X(G)=∑ v i 1 v i 2 v i 3 ...v i n+1 (1/d i 1 +d i 2 +...+d i n+1 ) , where the paths of length n in G are denoted by v i 1 , v i 2 , ... ,v i n+1 and the degree of each vertex vi is denoted by di. In this paper, we discuss third connectivity and third sum-connectivity indices of diamond-like networks and compute analytical closed results of these indices for diamond-like networks.

Different approaches have been used to convert the waste materials into a clean syngas or other chemicals such as methanol. Among them, pyrolysis is a good candidate to produce the synthesis gas an...

LetG=V,Ebe a simple connected graph,w∈Vbe a vertex, ande=uv∈Ebe an edge. The distance between the vertexwand edgeeis given byde,w=mindw,u,dw,v, A vertexwdistinguishes two edgese1,e2∈Eifdw,e1≠dw,e2. A setSis said to be resolving if every pair of edges ofGis distinguished by some vertices ofS. A resolving set with minimum cardinality is the basis forG, and this cardinality is the edge metric dimension ofG, denoted byedimG. It has already been proved that the edge metric dimension is an NP-hard problem. The main objective of this article is to study the edge metric dimension of some families of wheel-related graphs and prove that these families have unbounded edge metric dimension. Moreover, the results are compared with the metric dimension of these graphs.