ABSTRACT Let G = (V, E) be a simple graph. A set SíV is a dominating set of G, if every vertex in V-S is adjacent to atleast one vertex in S. Letbe the square of the Pathand letdenote the family of all dominating sets ofwith cardinality i. Let. In this paper, we obtain a recursive formula for. Using this recursive formula, we construct the polynomial, , which we call domination polynomial ofand obtain some properties of this polynomial.
Cite this paper
A. Vijayan and K. Gipson, "Dominating Sets and Domination Polynomials of Square of Paths," Open Journal of Discrete Mathematics, Vol. 3 No. 1, 2013, pp. 60-69. doi: 10.4236/ojdm.2013.31013.
 S. Alikhani and Y.-H. Peng, “Introduction to Domination Polynomial of a Graph,” .arXiv:0905.2251v1[math.co], 2009.
 S. Alikhani and Y.-H. Peng, “Domination Sets and Domination Polynomials of Paths,” International Journal of Mathematics and Mathematical Sciences, Vol. 2009, 2009, Article ID: 542040.
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