Signed edge majority domination numbers in graphs

The open neighborhood NG(e) of an edge e in a graph G is the set consisting of all edges having a common end-vertex with e and its closed neighborhood is NG[e] = NG(e) ∪ {e}. Let f be a function on E(G), the edge set of G, into the set {−1, 1}. If ∑x∈NG[e] f(x) ≥ 1 for at least a half of the edges e ∈ E(G), then f is called a signed edge majority dominating function of G. The minimum of the values of ∑ e∈E(G) f(e), taken over all signed edge majority dominating functions f of G, is called the signed edge majority domination number of G and is denoted by γ sm(G). In this paper we initiate the study of signed edge majority domination in graphs. We first use an existing upper bound for the majority domination numbers of graphs to present an upper bound for signed edge majority domination numbers of graphs. Then we establish a sharp lower bound for the signed edge majority domination number of a graph. ∗ Research supported by a Faculty Research Grant, University of West Georgia. 292 H. KARAMI, S.M. SHEIKHOLESLAMI AND A. KHODKAR