Geodesic
Roots of independence polynomials of well covered graphs
Journal of Algebraic Combinatorics, Tome 11 (2000) no. 3, pp. 197-210.

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Summary: Let G be a well covered graph, that is, all maximal independent sets of G have the same cardinality, and let i $_{k}$ denote the number of independent sets of cardinality k in G. We investigate the roots of the independence polynomial $i(G, x) = sum$ i $_{k}$x $^{k}$. In particular, we show that if G is a well covered graph with independence number $beta$, then all the roots of $i(G, x)$ lie in in the disk |z| $lebeta$ (this is far from true if the condition of being well covered is omitted). Moreover, there is a family of well covered graphs (for each $beta$) for which the independence polynomials have a root arbitrarily close to - $beta$.
Keywords: graph, independence, polynomial, root, well covered 
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     author = {Brown, J.I. and Dilcher, K. and Nowakowski, R.J.},
     title = {Roots of independence polynomials of well covered graphs},
     journal = {Journal of Algebraic Combinatorics},
     pages = {197--210},
     publisher = {mathdoc},
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     number = {3},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2000__11_3_a4/}
}
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Brown, J.I.; Dilcher, K.; Nowakowski, R.J. Roots of independence polynomials of well covered graphs. Journal of Algebraic Combinatorics, Tome 11 (2000) no. 3, pp. 197-210. http://geodesic.mathdoc.fr/item/JAC_2000__11_3_a4/