  The independence polynomial $I(G, x)$ of a graph $G$ is the polynomial in
variable $x$ in which the coefficient $a_n$ on $x^n$ gives the number of
independent subsets $S \subseteq V(G)$ of vertices of $G$ such that $|S| = n$.
$I(G, x)$ is unimodal if there is an index $\mu$ such that that $a_0 \leq a_1
\leq$...$\leq a_{\mu-1} \leq a_{\mu} \geq a_{\mu +1} \geq$...$\geq a_{d-1} \geq
a_d$ While the independence polynomials of many families of graphs with highly
regular structure are known to be unimodal, little is known about less
regularly structured graphs. We analyze the independence polynomials of a large
infinite family of trees without regular structure and show that these
polynomials are unimodal through a combinatorial analysis of the polynomials
coefficients.
