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Graphs and Combinatorics

, Volume 20, Issue 1, pp 105–119 | Cite as

On Graphs Determined by Their Tutte Polynomials

  • Anna de Mier
  • Marc Noy
Article

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.

Keywords

Tutte Polynomial Complete Multipartite Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Tokyo 2004

Authors and Affiliations

  1. 1.Departament de Matemàtica Aplicada IIUniversitat Politècnica de CatalunyaBarcelonaSpain

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