Vietnam Journal of Mathematics

, Volume 43, Issue 4, pp 755–769 | Cite as

Dependence Polynomials of some Graph Operations

  • Zahra Shiri
  • Ali Reza AshrafiEmail author


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 2c 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.


Dependence 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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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematical SciencesUniversity of KashanKashanIslamic Republic of Iran

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