English

The Domination Polynomials of Cubic graphs of order 10

Combinatorics 2009-05-21 v1

Abstract

Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G,x)=\sum_{i=\gamma(G)}^{n} d(G,i) x^{i}, where d(G,i) is the number of dominating sets of G of size i, and \gamma(G) is the domination number of G. In this paper we study the domination polynomials of cubic graphs of order 10. As a consequence, we show that the Petersen graph is determined uniquely by its domination polynomial.

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Cite

@article{arxiv.0905.3281,
  title  = {The Domination Polynomials of Cubic graphs of order 10},
  author = {Saieed Akbari and Saeid Alikhani and Yee-hock Peng},
  journal= {arXiv preprint arXiv:0905.3281},
  year   = {2009}
}

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13 pages