Turkish Journal of Mathematics
DOI
10.3906/mat-1002-141
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
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
