Signed edge k-subdomination numbers in graphs

The closed neighborhood NG[e] of an edge e in a graph G is the set consisting of e and of all edges having a common end-vertex with e. Let f be a function on E(G), the edge set of G, into the set {−1, 1}. If ∑ x∈N [e] f(x) ≥ 1 for at least k edges e of G, then f is called a signed edge k-subdominating function of G. The minimum of the values ∑ e∈E(G) f(e), taken over all signed edge k-subdominating function f of G, is called the signed edge k-subdomination number of G and is denoted by γ′ ks(G). In this note we initiate the study of the signed edge k-subdomination in graphs and present some (sharp) bounds for this parameter.