On Graphs Determined by Their Tutte Polynomials

Authors:
Anna de Mier;Marc Noy
Affiliations:
Universitat Politècnica de Catalunya, Departament de Matemàtica Aplicada II, Spain;Universitat Politècnica de Catalunya, Departament de Matemàtica Aplicada II, Spain
Venue:
Graphs and Combinatorics
Year:
2004

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Abstract

We say that a graph G is T-unique if any other graph having the same Tutte polynomial as G is necessarily isomorphic to G. In this paper we show that several well-known families of graphs are T-unique: wheels, squares of cycles, complete multipartite graphs, ladders, Möbius ladders, and hypercubes. In order to prove these results, we show that several parameters of a graph, like the number of cycles of length 3, 4 and 5, and the edge-connectivity are determined by its Tutte polynomial.