Hosoya polynomials of hexagonal triangles and trapeziums

The Hosoya polynomial of a graph G with vertex set V(G) is defined as H(G,x) = ∑{u,v}⊆V(G) xdG (u,v) in variable x, where the sum is over all unordered pairs {u, v} of vertices in G, dG(u, v) is the distance of two vertices u, v in G. In this paper, we investigate Hosoya polynomials of hexagonal trapeziums, tessellations of congruent regular hexagons shaped like trapeziums and give their explicit analytical expressions. As a special case, Hosoya polynomials of hexagonal triangles are obtained. Also, the three well-studied topological indices: Wiener index, hyper-Wiener index and Tratch-Stankevitch-Zefirov index, of hexagonal trapeziums can be easily obtained. Copyright © 2014 MATCH Communications in Mathematical and in Computer Chemistry.