  Let $P(G,q)$ be the chromatic polynomial for coloring the $n$-vertex graph
$G$ with $q$ colors, and define $W=\lim_{n \to \infty}P(G,q)^{1/n}$. 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 $q \in {\mathbb C}$, we determine the accumulation sets of the
chromatic zeros constituting the continuous loci of points on which $W$ is
nonanalytic. Various families of graphs with the property that the chromatic
zeros and/or their accumulation sets (i) include support for $Re(q) < 0$; (ii)
bound regions and pass through $q=0$; and (iii) are noncompact are discussed,
and the role of boundary conditions is analyzed. Some corresponding results are
presented for Potts model partition functions for nonzero temperature,
equivalent to the full Tutte polynomials for various families of graphs.
