on the signed roman edge k-domination in graphs

Let k ≥ 1 be an integer, and g = (v, e) be a finite and simple graph. the closed neighborhood ng[e] of an edge e in a graph g is the set consisting of e and all edges having a common end-vertex with e. a signed roman edge k-dominating function (srekdf) on a graph g is a function f : e → {−1, 1, 2} satisfying the conditions that (i) for every edge e of g, σ x∈n[e] f(x) ≥ k and (ii) every edge e for which f(e) = −1 is adjacent to at least one edge e 0 for which f(e′) = 2. the minimum of the values σ e∈e f(e), taken over all signed roman edge k-dominating functions f of g, is called the signed roman edge k-domination number of g and is denoted by γ′srk(g). in this paper we establish some new bounds on the signed roman edge k-domination number.