Dergiler / Turkish Journal of Mathematics / 2011 / Cilt: 35 - Sayı: 3
Domination polynomials of cubic graphs of order 10
- Sayfa
- 355–366
- DOI
- —
Özet
Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G,x)=\sumi=g(G)n d(G,i) xi, where d(G,i) is the number of dominating sets of G of size i, and g(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.
Abstract
Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G,x)=\sumi=g(G)n d(G,i) xi, where d(G,i) is the number of dominating sets of G of size i, and g(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.