  The independence polynomial $i(G,x)$ of a graph $G$ is the generating
function of the numbers of independent sets of each size. A graph of order $n$
is very well-covered if every maximal independent set has size $n/2$. Levit and
Mandrescu conjectured that the independence polynomial of every very
well-covered graph is unimodal (that is, the sequence of coefficients is
nondecreasing, then nonincreasing). In this article we show that every graph is
embeddable as an induced subgraph of a very well-covered graph whose
independence polynomial is unimodal, by considering the location of the roots
of such polynomials.
