Discrete Mathematics
On the numbers of independent k-sets in a claw free graph
Journal of Combinatorial Theory Series B
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
Variations sur le thème E+E=XY
Advances in Applied Mathematics
On the Location of Roots of Independence Polynomials
Journal of Algebraic Combinatorics: An International Journal
Matching Polynomials And Duality
Combinatorica
Average independence polynomials
Journal of Combinatorial Theory Series B
On Dependency Graphs and the Lattice Gas
Combinatorics, Probability and Computing
The roots of the independence polynomial of a clawfree graph
Journal of Combinatorial Theory Series B
On the dependence polynomial of a graph
European Journal of Combinatorics
Journal of Combinatorial Theory Series B
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The independence polynomial of a graph G is the polynomial @?"Ix^|^I^|, summed over all independent subsets I@?V(G). We show that if G is clawfree, then there exists a Mehler formula for its independence polynomial. This was proved for matching polynomials in Lass (2004) [19] and extends the combinatorial proof of the Mehler formula found by Foata (1978) [9]. It implies immediately that all the roots of the independence polynomial of a clawfree graph are real, answering a question posed by Hamidoune (1990) [14] and Stanley (1998) [28] and solved by Chudnovsky and Seymour (2007) [6]. We also prove a Mehler formula for the multivariate matching polynomial, extending results of Lass (2004) [19].