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

A. Vijayan¹, J. Sherin Beula^2*

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

DOI: 10.4236/ojdm.2015.54007                

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

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