Chromatic polynomials and their zeros and asymptotic limits for families of graphs

AbstractLet P(G,q) be the chromatic polynomial for coloring the n-vertex graph G with q colors, and define W=limn→∞P(G,q)1/n. Besides their mathematical interest, these functions are important in statistical physics. We give a comparative discussion of exact calculations of P and W for a variety of recursive families of graphs, including strips of regular lattices with various boundary conditions and homeomorphic expansions thereof. Generalizing to q∈C, we determine the accumulation sets of the chromatic zeros, which constitute the continuous loci of points on which W is nonanalytic. Conditions for the chromatic zeros and their accumulation set to (i) include support for Re(q)