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The Domination Polynomials of Cubic graphs of order 10

By Saieed Akbari, Saeid Alikhani and Yee-hock Peng


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.Comment: 13 page

Topics: Mathematics - Combinatorics, 05C60
Year: 2009
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