Hosoya Polynomials and Wiener Indices of Semifull Graph for Some Special Graphs

Let G be a finite simple connected graph of order p, size q, and block B=B(G). The semifull graph of G is a graph that has a vertex set V(G)∪E(G)∪B(G). So that any two vertices in the semifull graph of G are adjacent if any two vertices are adjacent in G, or any two edges are adjacent in G, or any two blocks are adjacent in G, or any vertex incident on edge or block. It was found that Hosoya polynomial, Wiener index, and average distance of a semifull graph are for some special graphs such as star, wheel, path, and cycle graphs, in addition to specifying the diameter for each of the resulting graphs.