Steiner Distance Polynomial of Graph

Abstract

The Steiner n-distance polynomial of a connected graph G, W_n(G;x), is defined as  sM_n(G,k)x^km where M_n(G, k) is the number of n-sets of vertices of G that are of n-distance K. Such polynomials W_n(G;x) are obtained for some special graphs and for compound graph G1 • G2 and G1:G2. Moreover, we give an upper bound for the average n-distance µ_n(G)