  We calculate the chromatic polynomials $P$ for $n$-vertex strip graphs of the
form $J(\prod_{\ell=1}^m H)I$, where $J$ and $I$ are various subgraphs on the
left and right ends of the strip, whose bulk is comprised of $m$-fold
repetitions of a subgraph $H$. The strips have free boundary conditions in the
longitudinal direction and free or periodic boundary conditions in the
transverse direction. This extends our earlier calculations for strip graphs of
the form $(\prod_{\ell=1}^m H)I$. We use a generating function method. From
these results we compute the asymptotic limiting function $W=\lim_{n \to
\infty}P^{1/n}$; for $q \in {\mathbb Z}_+$ this has physical significance as
the ground state degeneracy per site (exponent of the ground state entropy) of
the $q$-state Potts antiferromagnet on the given strip. In the complex $q$
plane, $W$ is an analytic function except on a certain continuous locus ${\cal
B}$. In contrast to the $(\prod_{\ell=1}^m H)I$ strip graphs, where ${\cal B}$
(i) is independent of $I$, and (ii) consists of arcs and possible line segments
that do not enclose any regions in the $q$ plane, we find that for some
$J(\prod_{\ell=1}^m H)I$ strip graphs, ${\cal B}$ (i) does depend on $I$ and
$J$, and (ii) can enclose regions in the $q$ plane. Our study elucidates the
effects of different end subgraphs $I$ and $J$ and of boundary conditions on
the infinite-length limit of the strip graphs.
