On the Location of Roots of Independence Polynomials

Authors:
J. I. Brown;C. A. Hickman;R. J. Nowakowski
Affiliations:
Department of Mathematics and Statistics and Faculty of Computer Science, Dalhousie University, Halifax, Canada B3H 3J5;The Fields Institute for Research in Mathematical Sciences, Toronto, Canada M5T 3J1;Department of Mathematics and Statistics, Dalhousie University, Halifax, Canada B3H 3J5
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2004

Citing 8
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Abstract

The independence polynomial of a graph G is the function i(G, x) = 驴 k驴0 i k x k, where i k is the number of independent sets of vertices in G of cardinality k. We prove that real roots of independence polynomials are dense in (驴驴, 0], while complex roots are dense in 驴, even when restricting to well covered or comparability graphs. Throughout, we exploit the fact that independence polynomials are essentially closed under graph composition.