Distance τ -polynomial and edge distance τ -polynomial of graphs

Abstract

The distance τ -polynomial D(G, x) of a graph G = (V, E) is defined as D(G, x) = (n2X)k = 0τkxk, where τk is the number of vertices with τG(u) = X x∈V (G)dG(u, x) = k, ∀u ∈ V (G). In this paper, we seek to find the distance τ -polynomial and similarly, edge distance τ -polynomial of some graph families and graph operations.