Signed majority edge domination in graphs

Abstract

Let G = (V, E) be a nonempty graph. For any real valued function f : E → ℝ and D ⊆ E, let f(D) = Σ_eεD f(e). A function f : E → {-1,1} defined on the edges of G is called a signed majority edge dominating function (SMEDF) if the sum of its function values over at least half the closed edgeneighborhood is at least one. That is, for at least half the edges e ε E, f(N[e]) ≥ 1, where N[e] consists of e and every edge adjacent to e. The signed majority edge domination number of a graph G is γ_maj(G) = min {f(E)\ f is a SMEDF of G}. In this paper, the signed majority edge domination number for several class of graphs are determined and some bounds of signed majority edge domination number are obtained.