Tutte polynomial expansions for 2-separable graphs

Let ^G be a graph obtained from a graph G with no loops or coloops by replacing each edge e = uw of G by a connected graph He that has only the vertices u and w in common with the rest of ^G. Two mutually dual formulas are proved for the Tutte polynomial of ^G in terms of parameters of the graphs He and (in the one case) ow polynomials of subgraphs of G or (in the other case) tension polynomials of contractions of G. This generalizes the results of Read and Whitehead on homeomorphism classes of graphs. c 2002 Elsevier Science B.V. All rights reserved.

• Type: Journal
• Year: 2002
• Where: DM
• Authors: Douglas R. Woodall
• Keywords: Connected Graph, DM 2002, Dual Formulas, Polynomials