Some new evaluations of the Tutte polynomial

Interpretations for evaluations of the Tutte polynomial T(G; x, y) of a graph G are given at a number of points on the hyperbolae H_q = {(x,y) : (x-1)(y-1)=q}, for q a positive integer - points at which there are usually no other similarly meaningful graphical interpretations. Further, when q is a prime power, an alternative interpretation for the evaluation of the Tutte polynormal at (1-q,0) is presented, more familiarly known as the point which gives the number of proper vertex q-colourings of G. (C) 2005 Elsevier Inc. All rights reserved.