On minus edge domination in graphs

Abstract

Let G = (V, E) be a nonempty graph. A three-valued function f : E → {-1,0,1} defined on the edges of G is called a minus edge dominating function (MEDF) if the sum of its function values over any closed edgeneighborhood is at least one. That is, for any edge e ε E, f(N[e]) ≥ 1, where N[e] consists of e and every edge adjacent to e. The weight of the function f is f(E) = Σ_eεE f(e)- The minus edge domination number of a graph G, denoted γ (G), equals the minimum weight of an MEDF of G. In this paper, the minus edge domination number for several class of graphs are determined and some bounds of minus edge domination number are obtained.