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arXiv · 0905.3281

The Domination Polynomials of Cubic graphs of order 10

Saieed Akbari·Saeid Alikhani·Yee-hock Peng
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Abstract

Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G,x)=\sum_{i=γ(G)}^{n} d(G,i) x^{i}, where d(G,i) is the number of dominating sets of G of size i, and γ(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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Saieed Akbari, Saeid Alikhani, Yee-hock Peng. 2009-05-20. The Domination Polynomials of Cubic graphs of order 10. https://arxiv.org/abs/0905.3281

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