On the Location of Roots of Independence Polynomials
نویسنده
چکیده
The independence polynomial of a graph G is the function i(G, x) = ∑k≥0 ik xk , where ik 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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