Domination polynomials of cubic graphs of order 10

Authors: SAEID ALIKHANI, YEE-HOCK PENG

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.

Keywords: Domination polynomial, equivalence class, petersen graph, cubic graphs

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