| Affiliation: | a Center for Combinatorics, LPMC, Nankai University, Tianjin, China
b Department of Mathematics, University of Mississippi, MS, USA
c Department of Mathematics and Statistics, Thompson Rivers University, Kamloops, BC, Canada |
| Abstract: | A graph G is called T-unique if any other graph having the same Tutte polynomial as G is isomorphic to G. Recently, there has been much interest in determining T-unique graphs and matroids. For example, de Mier and Noy [A. de Mier, M. Noy, On graphs determined by their Tutte polynomials, Graphs Combin. 20 (2004) 105-119; A. de Mier, M. Noy, Tutte uniqueness of line graphs, Discrete Math. 301 (2005) 57-65] showed that wheels, ladders, Möbius ladders, square of cycles, hypercubes, and certain class of line graphs are all T-unique. In this paper, we prove that the twisted wheels are also T-unique. |
