Graph products with log-concave independence polynomials
نویسندگان
چکیده
A stable set in a graph G is a set of pairwise non-adjacent vertices. The independence polynomial of G is I(G;x) = s0+s1x+s2x 2 +...+sαx α , where α = α(G) is the cardinality of a maximum stable of G, while sk equals the number of stable sets of size k in G (Gutman and Harary, 1983). Hamidoune, 1990, showed that for every claw-free graph G (i.e., a graph having no induced subgraph isomorphic to K1,3), its independence polynomial is log-concave, that is, (sk) 2 ≥ sk-1 • sk+1 holds for every k∈{1,...,α-1}. Using this result, we investigate log-concavity of I(G;x), where G is a product (Cartesian, Kronecker, normal, edge-join, corona, composition) of some other graphs. Key-Words: stable set, independence polynomial, claw-free, graph products, unimodal, log-concave
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