Domination polynomials of cubic graphs of order 10

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.

Anahtar Kelimeler:

Domination polynomial, equivalence class, petersen graph, cubic graphs

Domination polynomials of cubic graphs of order 10

Keywords:

Domination polynomial, equivalence class, petersen graph, cubic graphs,

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Akbari, S. and Aalipour, G.: On the D-eqnivalence class of complete bipartite graphs, Ars Combin., to appear.
Akbari, S., Alikhani, S. and Peng, Y. H.: Characterization of graphs using Domination Polynomial, European J. Combin, Vol 31, 1714-1724 (2010).
Akbari, S. and Oboudi, M. R.: Cycles are determined by their domination polynomials, Ars combin., to appear.
Alikhani, S. and Peng, Y. H.: Dominating sets and Domination Polynomials of Certain Graphs, II, Opuscula Mathematica, 30, No 1, 37-51 (2010).
Alikhani, S. and Peng, Y. H.: Dominating sets and domination polynomials of cycles, Global Journal of Pure and Applied Mathematics, 4, n0 2, 151-162 (2008).
Alikhani, S. and Peng, Y. H.: Dominating sets and Domination Polynomials of Paths, International Journal of Mathematics and Mathematical Science, Vol 2009, Article ID 542040 (2009).
Alikhani, S. and Peng, Y. H.: Introduction to Domination polynomial of a graph, Ars Combin., to appear.
Dong, F. M., Koh, K. M. and Teo, K. L.: Chromatic polynomials and chromaticity of graphs, World ScientiŞc Publishing Co. Pte. Ltd 2005.
Haynes, T. W., Hedetniemi, S. T. and Slater, P. J.: Fundamentals of Domination in Graphs, Marcel Dekker, NewYork 1998.
Khosrovshahi, G. B., Maysoori, Ch. and Tayfeh—Rezaie, B.: A Note on 3-Factorizations of K10, J. Combin. Designs 9, 379-383 (2001).
Saeid ALIKHANI Received: 17.02.2010
Department of Mathematics, Yazd University 89195-741 Yazd—IRAN
e—mail: alikhani©yazduni. ac. ir Yee—Hock PENG
Institute for Mathematical Research,
University Putra Malaysia
UPM Serdang—MALAYSIA