On Szeged Polynomial of a Graph

on szeged polynomial of a graph

On the Roots of Hosoya Polynomial of a Graph

Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...

A N‎ote on Revised Szeged ‎Index of ‎Graph ‎Operations

Let $G$ be a finite and simple graph with edge set $E(G)$‎. ‎The revised Szeged index is defined as‎ ‎$Sz^{*}(G)=sum_{e=uvin E(G)}(n_u(e|G)+frac{n_{G}(e)}{2})(n_v(e|G)+frac{n_{G}(e)}{2}),$‎ ‎where $n_u(e|G)$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$ and‎ ‎$n_{G}(e)$ is the number of‎ ‎equidistant vertices of $e$ in $G$‎. ‎In this paper...

Some New Results On the Hosoya Polynomial of Graph Operations

The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiene...

on the roots of hosoya polynomial of a graph

let g = (v, e) be a simple graph. hosoya polynomial of g isd(u,v)h(g, x) = {u,v}v(g)x , where, d(u ,v) denotes the distance between vertices uand v. as is the case with other graph polynomials, such as chromatic, independence anddomination polynomial, it is natural to study the roots of hosoya polynomial of a graph. inthis paper we study the roots of hosoya polynomials of some specific graphs.

The Edge Szeged Polynomial of Graphs

The edge Szeged polynomial of a graph G is defined as Sze(G,x) = ( ) ( ) , u v m e m e e uv x = ∑ where mu(e) is the number of edges of G lying closer to u than to v and mv(e) is the number of edges of G lying closer to v than to u. In this paper the main properties of this newly proposed polynomial are investigated. We also compute this polynomial for some classes of well-known graphs. Finally...