let g be a simple graph. the hosoya polynomial of g is ( , ) ,( , ) = { , } ( ) xd u v h g x  u v v gwhere d(u,v) denotes the distance between vertices u and v . the dendrimer nanostar is apart of a new group of macromolecules. in this paper we compute the hosoya polynomial foran infinite family of dendrimer nanostar. as a consequence we obtain the wiener index andthe hyper-wiener index of th...

Given a molecular graph G, the Hosoya index Z(G) of G is defined as the total number of the matchings of the graph. Let Bn denote the set of bicyclic graphs on n vertices. In this paper, the minimal, the second-, the third-, the fourth-, and the fifth-minimal Hosoya indices of bicyclic graphs in the set Bn are characterized.

Akio Hosoya, Thomas Buchert, 1, 3 and Masaaki Morita 5 Department of Physics, Tokyo Institute of Technology, Oh–Okayama, Meguro–ku, Tokyo 152–0033, Japan Theoretische Physik, Ludwig–Maximilians–Universität, Theresienstr. 37, D–80333 München, Germany Department of Physics and Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, Tokyo 113–0033, Japan Depart...

Let G be a simple graph and let S(G) be the subdivision graph of G, which is obtained from G by replacing each edge of G by a path of length two. In this paper, by the Principle of Inclusion and Exclusion we express the matching polynomial and Hosoya index of S(G) in terms of the matchings of G. Particularly, if G is a regular graph or a semi-regular bipartite graph, then the closed formulae of...

Abstract Many chemical indices have been invented in theoretical chemistry, such as Wiener index, Merrifield-Simmons index, Hosoya index, spectral radius and Randić index, etc. The extremal trees and unicyclic graphs for these chemical indices are interested in existing literature. Let G be a molecular graph (called a cacti), which all of blocks of G are either edges or cycles. Denote G (n, r) ...

The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, we give formula for Merrifield-Simmons and Hosoya indices of some classes of cartesian product of two graphs K{_2}×H, where H is a path graph P{_n}, cyclic graph C{_n}, or star gra...

Let G = (V (G), E(G)) be a graph. An m−matchings of G is a set of edges of size m in which any two edges are mutually independent. Denote by z(G,m) the number of m−matchings of G. Let z(G) be the total number of matchings in G, namely z(G) = bn 2 c ∑ m=1 z(G,m). It’s well-known that z(G) are also named as Hosoya index. Let Tn,d be the set of trees of on n vertices with diameter d. In this paper...