Abstract
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.
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