## Graph Polynomials: From Recursive Definitions To Subset Expansion Formulas

##### Authors
Godlin, Benny
Katz, Emilia
Makowsky, Johann A.
##### Description
Many graph polynomials, such as the Tutte polynomial, the interlace polynomial and the matching polynomial, have both a recursive definition and a defining subset expansion formula. In this paper we present a general, logic-based framework which gives a precise meaning to recursive definitions of graph polynomials. We then prove that in this framework every recursive definition of a graph polynomial can be converted into a subset expansion formula.
Comment: 25 pages, 2 figures
##### Keywords
Computer Science - Logic in Computer Science, Computer Science - Discrete Mathematics