On Tutte polynomial uniqueness of twisted wheels

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.