Counterexamples to a conjecture of Balasubramanian and Parthasarathy

Abstract

In 1980, Balasubramanian and Parthasarathy introduced the bivariate permanent polynomials of graphs and conjectured that this graph polynomial is a graph characterising polynomial, that is, any two graphs with the same bivariate permanent polynomial are isomorphic. In this note, we give counter examples to this conjecture.

5 pages, 1 figure