  We exhibit non-switching-isomorphic signed graphs that share a common
underlying graph and common chromatic polynomials, thereby answering a question
posed by Zaslavsky. For various joins of all-positive or all-negative signed
complete graphs, we derive a closed-form expression for their chromatic
polynomials. As a generalisation of the chromatic polynomials for a signed
graph, we introduce a new pair of bivariate chromatic polynomials. We establish
recursive dominating-vertex deletion formulae for these bivariate chromatic
polynomials. Finally, we show that for certain families of signed threshold
graphs, isomorphism is equivalent to the equality of bivariate chromatic
polynomials.
