Dependence Polynomials of some Graph Operations
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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.
KeywordsDependence polynomial Graph operation Subgraph division Johnson graph Kneser graph
Mathematics Subject Classification (2010)05C31 05C76 05C90
The authors are greatly indebted to the referee for his/her suggestions leaded us to improve the paper. The research of the authors are partially supported by the University of Kashan under grant no 364988/46.
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