Average independence polynomials

Authors:
J. I. Brown;R. J. Nowakowski
Affiliations:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5;Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
Venue:
Journal of Combinatorial Theory Series B
Year:
2005

Citing 4
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Abstract

The independence polynomial of a graph G is the function i(G, x) = Σ k ≥ 0 ik xk, where ik is the number of independent sets of vertices in G of cardinality k. We investigate here the average independence polynomial, where the average is taken over all independence polynomials of (labeled) graphs of order n. We prove that while almost every independence polynomial has a nonreal root, the average independence polynomials always have all real, simple roots.