Let G be a simple graph without isolated vertices with vertex set V(G) and edge set E(G) and let k be a positive integer. A function f:E(G)⟶{−1,1} is said to be a signed star k-dominating function on G if ∑e∈E(v)f(e)≥k for every vertex v of G, where E(v)={uv∈E(G)∣u∈N(v)}. A set {f1,f2,…,fd} of signed star k-dominating functions on G with the property that ∑di=1fi(e)≤1 for each e∈E(G), is called a signed star k-dominating family (of functions) on G. The maximum number of functions in a signed star k-dominating family on G is the signed star k-domatic number of G, denoted by dkSS(G).