Dominating Sets and Domination Polynomial of Wheels
Abstract
Let be a simple graph. set is a dominating set of , if every vertex in is adjacent to at least one vertex in . Let be wheel with order n. Let be the family of dominating sets of a wheels with cardinality , and let . In this paper, we construct , and obtain a recursive formula for . Using this recursive formula, we consider the polynomial , which we call domination polynomial of wheels and obtain some properties of this polynomial.
References
S. Alikhani, Y. H. Peng, Dominating Sets and Domination Polynomial of Cycles, arXiv preprint arXiv:0905.3268 (2009).
S. Alikhani, Y. H. Peng, Dominating Sets and Domination Polynomial of Certain Graphs, II, Opuscula Mathematica 30, no. 1 (2010): 37-51.
.M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completness. Freeman, New York, 1979.
S. Sh. Kahat, A. M. Khalaf and Roslan Hasni, Dominating Sets and Domination Polynomial of stars, Australian Journal of Basic and Applied Sciences, June 2014.
T.W. Haynes, S.T. Hedetniemi, P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
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