The Domination Polynomials of Cubic graphs of order 10

Akbari, Saieed; Alikhani, Saeid; Peng, Yee-hock

The Domination Polynomials of Cubic graphs of order 10

Authors

Akbari, Saieed

Alikhani, Saeid

Peng, Yee-hock

Description

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.
13 pages