The Hosoya Index of Graphs Formed by a Fractal Graph

Abstract

The computational complexity of the Hosoya index of a given graph is NP-Complete. Let [Formula: see text] be the graph constructed from [Formula: see text] by a triangle instead of all vertices of the initial graph [Formula: see text]. In this paper, we characterize the Hosoya index of the graph [Formula: see text]. To our surprise, it shows that the Hosoya index of [Formula: see text] is thoroughly given by the order and degrees of all the vertices of the initial graph [Formula: see text].

Reverse Zagreb and Reverse Hyper-Zagreb Indices for Crystallographic Structure of Molecules

“…Topological indices enable us to collect information about algebraic structures and give us a mathematical approach to understand the properties of algebraic structures. Here, we will discuss some newly introduced first and second reverse Zagreb indices, hyper-Zagreb indices, and their polynomials for the crystallographic structure of molecules [1][2][3][4][5][6][7][8][9].…”

Topological Indices of Certain Transformed Chemical Structures

“…Baig et al found the topological indices for poly oxide, poly silicate, DOX, and DSL networks in [5]. Liu et al found the different topological indices for Eulerian graphs, fractal graphs, and generalized Sierpinski networks in [6][7][8].…”

On Generalized Topological Indices of Silicon-Carbon

“…A chemical structure can be represented by using graph theory, where vertices denote atoms and edges denote chemical bonds. Chemical graph theory is a branch of mathematical chemistry that it is a subject that connects mathematics, chemistry, and graph theory and solves problems arising in chemistry mathematically (for more details you can see [2][3][4][5][6][7][8]).…”

“…e topological indices of 2-dimensional silicon-carbons are computed in [12], in [13], Kwunet al On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si 2 C 3 − I [p, q] and Si 2 C3 − II [p, q], in [14], Imran [16], Kulli. F-indices of Chemical Networks, in [6], in [17], Gao et al the Redefined first, second and third Zagreb Indices of Titania Nanotubes TiO 2 [m, n] and in [18], Kang et al computed the topological indices of 2-dimensional silicon-carbon. For more details, see [19][20][21][22][23].…”