Keywords : n-Hosoya polynomial


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
 

The n-Hosoya Polynomials of the Composite of Some Special Graphs

Ahmed M. Ali

AL-Rafidain Journal of Computer Sciences and Mathematics, 2013, Volume 10, Issue 2, Pages 47-62
DOI: 10.33899/csmj.2013.163474

It is not easy to find the n-Hosoya polynomial of the compound graphs constructed in the form G1⊠G2 for any two disjoint connected graphs  and .Therefore, in this paper, we obtain n-Hosoya polynomial of G1⊠G2 when  is a complete graph and  is a special graph such as a complete graph, a bipartite complete, a wheel, or a cycle. The n-Wiener index of each such composite graph is also obtained in this paper.
 

The n-Hosoya Polynomial of 𝑊𝛼⊠ Cβ

Ahmed M. Ali; Haveen G. Ahmed

AL-Rafidain Journal of Computer Sciences and Mathematics, 2012, Volume 9, Issue 2, Pages 139-150
DOI: 10.33899/csmj.2012.163707

For a wheel  and a cycle  the composite graphs ⊠  is constructed from the union of  and  and  adding the edges  and  , where  is an edge of  and is an edge of . The n – diameter , the  n – Hosoya polynomial and the n – Wiener index of  ⊠  are obtained in this paper.