Wiener Index of Edge Thorny Graphs of Catacondensed Benzenoids

The Wiener index is a topological index of a molecular graph, defined as the sum of distances between all pairs of its vertices. Benzenoid graphs include molecular graphs of polycyclic aromatic hydrocarbons. An edge thorny graph G is constructed from a catacondensed benzenoid graph H by attaching new graphs to edges of a perfect matching of H. A formula for the Wiener index of G is derived. The index of the resulting graph does not contain distance characteristics of elements of H and depends on the Wiener index of H and distance properties of the attached graphs.

Characteristic Graph vs Benzenoid Graph

A characteristic graph is a tree representative of its corresponding benzenoid (cyclic) graph. It may contain necessary information of several properties of benzenoids. The PI-index of benzenoids and their characteristic graphs are compared by correlating it to a structural property (π-electron energy) of the benzenoids using MLR analysis. PI index being applicable to both trees and cyclic graphs, yielded required results for benzenoid and their characteristic graph.

On Connectivity Indices of an Infinite Family of the Linear Parallelogram of Benzenoid Graph

A topological index of a graph G is a numeric quantity related to G which is describe molecular graph G. In this paper the Atom Bond Connectivity (ABC) and Geometric-Arithmetic (GA) indices of an infinite class of the linear parallelogram of benzenoid graph.

Computing a Counting Polynomial of an Infinite Family of Linear Polycene Parallelogram Benzenoid Graph P(a,b)

Omega polynomial was defined by M.V. Diudea in 2006 as  where the number of edges co-distant with e is denoted by n(e). One can obtain Theta Θ, Sadhana Sd and Pi Πpolynomials by replacing xn(e) with n(e)xn(e), x|E|-n(e) and n(e)x|E|-n(e) in Omega polynomial, respectively. Then Theta Θ, Sadhana Sd and Pi Πindices will be the first derivative of Θ(x), Sd(x) and Π(x) evaluated at x=1. In this paper, Pi Π(G,x) polynomial and Pi Π(G) index of an infinite family of linear polycene parallelogram benzenoid graph P(a,b) are computed for the first time.

Computing the Omega polynomial of an infinite family of the linear parallelogram P(n,m)

Let G=(V,E) be a molecular graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges. The Omega polynomial Ω(G,x) was introduced by Diudea in 2006 and this defined as where m(G,c) the number of qoc strips of length c. In this paper, we compute the omega polynomial of an infinite family of the linear parallelogram P(n,n) of benzenoid graph.