Signed edge total k-subdomination numbers in graphs

Abstract

The open neighborhood N_G(e) of an edge e in a graph G is the set consisting 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 Σ _x∈NG(e) f (x) ≥ 1 for at least k edges e of G, then f is called a signed edge total k-subdominating function of G. The minimum of the values Σ_e∈E(G) f(e) taken over all signed edge total k-subdominating function f of G, is called the signed edge total k-subdomination number of G and is denoted by γ′_stk (G). In this note we initiate the study of the signed edge total k-subdomination in graphs and present some sharp bounds for this parameter.