Abstract
The independence polynomial of a graph G is the function i(G, x) = ∑ k≥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 (−∞, 0], while complex roots are dense in ℂ, even when restricting to well covered or comparability graphs. Throughout, we exploit the fact that independence polynomials are essentially closed under graph composition.
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Brown, J., Hickman, C. & Nowakowski, R. On the Location of Roots of Independence Polynomials. J Algebr Comb 19, 273–282 (2004). https://doi.org/10.1023/B:JACO.0000030703.39946.70
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DOI: https://doi.org/10.1023/B:JACO.0000030703.39946.70