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.
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Research partially supported by projects BFM2001-2340 and by CUR Gen. Cat. 1999SGR00356
Final version received: January 10, 2003
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Mier, A., Noy, M. On Graphs Determined by Their Tutte Polynomials. Graphs and Combinatorics 20, 105–119 (2004). https://doi.org/10.1007/s00373-003-0534-z
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DOI: https://doi.org/10.1007/s00373-003-0534-z