Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles - Open Journal of Discrete Mathematics

OJDM > Vol.5 No.4, October 2015

Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles ()

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DOI: 10.4236/ojdm.2015.54007 3,544 Downloads 4,938 Views Citations

Author(s)

A. Vijayan¹, J. Sherin Beula^2*

Affiliation(s)

¹Department of Mathematics, Nesamony Memorial Christian College, Marthandam, India.
²Department of Mathematics, Mar Ephraem College of Engineering & Technology, Marthandam, India.

ABSTRACT

Let G = (V, E) be a simple graph. A set S

E(G) is an edge-vertex dominating set of G (or simply an ev-dominating set), if for all vertices v V(G); there exists an edge eS such that e dominates v. Let

denote the family of all ev-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 edge-vertex domination polynomial of

(or simply an ev-domination polynomial of

) and obtain some properties of this polynomial.

KEYWORDS

ev-Domination Set, ev-Domination Number, ev-Domination Polynomials

Share and Cite:

Vijayan, A. and Sherin Beula, J. (2015) Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles. Open Journal of Discrete Mathematics, 5, 74-87. doi: 10.4236/ojdm.2015.54007.

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