On the Roots of σ-Polynomials

Given a graph G of order n, the σ -polynomial of G is the generating function σ (G, x ) = ∑ aix where ai is the number of partitions of the vertex set of G into i nonempty independent sets. Such polynomials arise in a natural way from chromatic polynomials. Brenti (Trans Am Math Soc 332 (1992), 729–756) proved that σ -polynomials of graphs with chromatic… CONTINUE READING