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 ∈ V(G) ,  S ⊆ V (G) , such that dn(v,S) = k , for each 0 ≤ k ≤ δn. 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 graphsare determined