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

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 e S 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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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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