On the evaluation of the Tutte polynomial at the points (1,-1) and (2,-1)

Abstract

C. Merino proved recently the following identity between evaluations of the Tutte polynomial of complete graphs: t($K_{n+2}$; 1,−1) = t($K_n$;2,−1). In this work we extend this result by giving a large class of graphs with this property, that is, graphs G such that there exist two vertices u and v with t(G;1,−1) = t(G−{u,v};2,−1). The class is described in terms of forbidden induced subgraphs and it contains in particular threshold graphs.