Clique polynomials and independent set polynomials of graphs
Selected papers of the 13th British Combinatorial Conference on British combinatorial conference
Discrete Mathematics - selected papers in honor of Adriano Garsia
Roots of Independence Polynomials of Well Covered Graphs
Journal of Algebraic Combinatorics: An International Journal
On the Location of Roots of Independence Polynomials
Journal of Algebraic Combinatorics: An International Journal
Average independence polynomials
Journal of Combinatorial Theory Series B
On Dependency Graphs and the Lattice Gas
Combinatorics, Probability and Computing
European Journal of Combinatorics
The roots of the independence polynomial of a clawfree graph
Journal of Combinatorial Theory Series B
On the roots of independence polynomials of almost all very well-covered graphs
Discrete Applied Mathematics
The circuit polynomial of the restricted rooted product G(Γ) of graphs with a bipartite core G
Discrete Applied Mathematics
On unimodality of independence polynomials of some well-covered trees
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
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A stable (or independent) set in a graph is a set of pairwise nonadjacent vertices thereof. The stability number@a(G) is the maximum size of stable sets in a graph G. The independence polynomial of G is I(G;x)=@?k=0@a(G)s"kx^k=s"0+s"1x+s"2x^2+...+s"@a"("G")x^@a^(^G^)(s"0@?1), where s"k is the number of stable sets of cardinality k in a graph G, and was defined by Gutman and Harary (1983) [13]. We obtain a number of formulae expressing the independence polynomials of two sorts of the rooted product of graphs in terms of such polynomials of constituent graphs. In particular, it enables us to build infinite families of graphs whose independence polynomials have only real roots.