Tutte polynomials for benzenoid systems with one branched hexagon

Benzenoid systems are natural graph representation of benzenoid hydrocarbons. Many chemically and combinatorially interesting indices and polynomials for bezenoid systems have been widely researched by both chemists and graph theorists. The Tutte polynomial of benzenoid chains without branched hexagons has already been computed by the recursive method. In this paper, by multiple recursion schema, an explicit expression for the Tutte polynomial of benzenoid systems with exactly one branched hexagon is obtained in terms of the number of hexagons on three linear or kinked chains. As a by-product, the number of spanning trees for these kind of benzenoid systems is determined.