On the Evaluation of the Tutte Polynomial at the Points (1, -1) and (2, -1).

Motivated by the identity t ( K 1, -1) = t ( K; 2, -1), where t( G; x, y) is the Tutte polynomial of a graph G, we search for graphs G having the property that there is a pair of vertices u, v such that t( G; 1, -1) = t( G - { u, v}; 2, -1). Our main result gives a sufficient condition for a graph to have this property; moreover, it describes the graphs for which the property still holds when each vertex is replaced by a clique or a coclique of arbitrary order. In particular, we show that the property holds for the class of threshold graphs, a well-studied class of perfect graphs. [ABSTRACT FROM AUTHOR]

Copyright of Annals of Combinatorics is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)