Dominating Sets and Domination Polynomials of Square of Paths - Open Journal of Discrete Mathematics

OJDM > Vol.3 No.1, January 2013

Dominating Sets and Domination Polynomials of Square of Paths ()

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DOI: 10.4236/ojdm.2013.31013 4,587 Downloads 8,109 Views Citations

Author(s)

A. Vijayan, K. Lal Gipson

Affiliation(s)

Department of Mathematics, Mar Ephraem College of Engineering and Technology, Kanayakumari District, India.
Department of Mathematics, Nesamony Memorial Christian College, Marthandam, India.

ABSTRACT

Let G = (V, E) be a simple graph. A set S í V is a dominating set of G, if every vertex in V-S is adjacent to at least one vertex in S. Let

be the square of the Path

and let

denote the family of all dominating sets of

with 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 of

and obtain some properties of this polynomial.

KEYWORDS

Domination Set; Domination Number; Domination Polynomials

Share and Cite:

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.

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