Signed star k-subdomination numbers in graphs

Let G be a simple graph without isolated vertex with vertex set V(G) and edge set E(G). A function f:E(G)@?{-1,1} is said to be a signed star k-subdominating function of G if @?"e"@?"E"("v")f(e)>=1 for at least k vertices v of G, where E(v)={uv@?E(G)|u@?N(v)}. The value min@?"e"@?"E"("G")f(e), taking over all signed star k-subdominating function f of G is called the signed star k-subdomination number of G and denoted by @c"S"S^k(G). In this paper we give some bounds on the signed star k-subdomination number of graphs.