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...

In mathematical chemistry, a particular attention is given to degree-based graph invariant. The Zagrebpolynomial is one of the degree based polynomials considered in chemical graph theory. A dendrimer isan artificially manufactured or synthesized molecule built up from branched units called monomers. Inthis note, the first, second and third Zagreb poly...

Let G be a graph with vertex and edge sets V(G) and E(G), respectively. As usual, the distance between the vertices u and v of a connected graph G is denoted by d(u,v) and it is defined as the number of edges in a minimal path connecting the vertices u and v. Throughout the paper, a graph means undirected connected graph without loops and multiple edges. In chemical graph theory, a molecular gr...

wiener index is a topological index based on distance between every pair of vertices in agraph g. it was introduced in 1947 by one of the pioneer of this area e.g, harold wiener. inthe present paper, by using a new method introduced by klavžar we compute the wiener andszeged indices of some nanostar dendrimers.