Schultz and Modified Schultz Polynomials for Edge – Identification Chain and Ring – for Pentagon and Hexagon Graphs

Abstract

In a connected graph G, the distance function between each pair of two vertices from a set vertex V(G) is a shortest distance between them and the vertex degree v, deg v, is the number of edges which are incident to the vertex v. The Schultz and modified Schultz polynomials of G are have defined as :Sc(G; x) = ∑( deg v + deg u) x d (u, v) and Sc ∗ (G; x) = ∑ (deg v. deg u) x d (u, v), respectively, where the summations are taken over all unordered pairs of distinct vertices in V(G) and d(u, v) is the distance between u and v in V(G). We shall find the general forms of Schultz and modified Schultz polynomials and indices of the edge – identification chain and ring – pentagon and hexagon graphs in the present work.

Generalized Schultz and Modified Schultz Polynomials for Some Special Graphs

“…There are a lot of papers that have been done to compute Schultz and modified Schultz polynomials and the indices for many graphs, for more information, see the references [6][7][8][9][10][11]. In this paper, we generalized the Schultz polynomial and modified the Schultz polynomial by taking all vertices degrees of the path, provided that the product of the length of the path with the sum of the degrees is a minimum, because of the importance of degrees as chemical bonds located on atoms and they are effects on the stability of the chemical compound.…”

Chromatic Schultz polynomial of certain graphs

“…Note that throughout this study, we use the chromatic colourings of the graphs under consideration. Motivated by the studies on Schultz polynomial of graphs (see [1,2,4,5]), we can now introduce the chromatic version of the Schultz polynomial as follows:…”

“…The chromatic versions of certain topological indices have been introduced in [8]. The Schultz polynomials and modified Schultz polynomials of graphs are some of such widely studied polynomials (see [1,2,4]).…”

Schultz and Modified Schultz Polynomials of Edges Induce Chain and Ring for Hexagonal Graphs

“…Farahani [8] discovered hosoya, (ScP) and (MScP) and their topological indices for benzene, followed by (ScP) and (MScP)of coronene polycyclic aromatic hydrocarbons in a subsequent study [9]. Many researchers have worked over the last decade to determine (ScP) and (MScP) and their indices for graphs consisting of chains and rings of special graphs with chemical applications [10], [19], [5], [11], [4], [1], [2].…”