The n-Hosoya Polynomials of the Square of a Path and of a Cycle

Abstract

The n-Hosoya polynomial of a connected graph G of order t is defined by:Hn(G;x)=∑Cn(G;x)xk, where, Cn(G,k) is the number of pairs (v,S), in which |S| = n -1, 3=< n =< t, v belong to V(G) , S sub set of V (G) , such that dn(v,S)= k , for each 0=< k=< n-diameter . In this paper, we find the n-Hosoya polynomial of the square of a path and of the square of a cycle. Also, the n-diameter and n-Wiener index of each of the two graphs are determined.