Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1002-141
Keywords
Domination polynomial, equivalence class, petersen graph, cubic graphs
First Page
355
Last Page
366
Recommended Citation
ALIKHANI, S, & PENG, Y (2011). Domination polynomials of cubic graphs of order 10. Turkish Journal of Mathematics 35 (3): 355-366. https://doi.org/10.3906/mat-1002-141
