Dependence Polynomials of some Graph Operations

Abstract

Suppose G is a simple graph and c k = c k (G) denotes the number of complete subgraphs of size k in G. Then the dependence polynomial of G is defined as f G (x) = 1 − c 1 x + c 2 x 2 − c 3 x 3 + · · · + (−1) n x n , where n is the size of the largest complete subgraph in G. In this paper, exact formulas for dependence polynomial of some graph operations are presented.