A matching M of a graph G is maximal if it not proper subset any other in G. Maximal matchings are much less known and researched than their maximum perfect counterparts. In this paper we present the recurrences generating functions for sequences enumerating two classes chemically interesting linear polymers: polyspiro chains benzenoid chains. We also analyze asymptotic behavior those determine...

The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.

The edge version of Szeged index and vertex version of PI index are defined very recently. They are similar to edge-PI and vertex-Szeged indices, respectively. The different versions of Szeged and PIindices are the most important topological indices defined in Chemistry. In this paper, we compute the edge-Szeged and vertex-PIindices of some important classes of benzenoid systems.