TITLE:
Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles
AUTHORS:
A. Vijayan, J. Sherin Beula
KEYWORDS:
ev-Domination Set, ev-Domination Number, ev-Domination Polynomials
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.5 No.4,
September
30,
2015
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.