Tutte polynomials of alternating polycyclic chains

摘要

The Tutte poynomial T(G; x, y) of a graph G is a two-variable graph polynomial, and it gives interesting information about the graph. Many chemically interesting polycyclic polymers can be modeled by uniform or non-uniform polycyclic graphs. In this paper, we consider the Tutte poynomial of several classes of alternating polycyclic chains which contain phenylene chains and their dicyclobutadieno derivatives as special cases. Further, explicit closed formula of the number of spanning trees, the number of spanning forests and the number of spanning connected subgraphs of phenylenes (resp. the dicyclobutadieno derivatives of phenylenes) are obtained.