Zaslavsky proved in 2012 that, up to switching isomorphism, there are six different
signed Petersen graphs and that they can be told apart by their chromatic
polynomials, by showing that the latter give distinct results when evaluated at 3. He
conjectured that the six different signed Petersen graphs also have distinct zero-free
chromatic polynomials, and that both types of chromatic polynomials have distinct
evaluations at
any positive integer. We developed and executed a computer
program (running in SAGE) that efficiently determines the number of proper
-colorings
for a given signed graph; our computations for the signed Petersen graphs confirm
Zaslavsky’s conjecture. We also computed the chromatic polynomials of all signed
complete graphs with up to five vertices.