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, SAEID and PENG, YEE-HOCK
(2011)
"Domination polynomials of cubic graphs of order 10,"
Turkish Journal of Mathematics: Vol. 35:
No.
3, Article 1.
https://doi.org/10.3906/mat-1002-141
Available at:
https://journals.tubitak.gov.tr/math/vol35/iss3/1
