Keywords : path square and cycle square

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

Ahmed M. Ali

AL-Rafidain Journal of Computer Sciences and Mathematics, 2021, Volume 15, Issue 1, Pages 13-24
DOI: 10.33899/csmj.2021.168250

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