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In this paper we introduce some Christoffel-Darboux type identities forindependence polynomials. As an application, we give a new proof of a theoremof M. Chudnovsky and P. Seymour, claiming that the independence polynomial of aclaw-free graph has only real roots. Another application is related to aconjecture of Merrifield and Simmons.

Christoffel-Darboux type identities for independence polynomial