Signed star domatic number of a graph

AbstractLet G be a simple graph without isolated vertices with vertex set V(G) and edge set E(G). A function f:E(G)⟶{−1,1} is said to be a signed star dominating function on G if ∑e∈E(v)f(e)≥1 for every vertex v of G, where E(v)={uv∈E(G)∣u∈N(v)}. A set {f1,f2,…,fd} of signed star dominating functions on G with the property that ∑i=1dfi(e)≤1 for each e∈E(G), is called a signed star dominating family (of functions) on G. The maximum number of functions in a signed star dominating family on G is the signed star domatic number of G, denoted by dSS(G).In this paper we study the properties of the signed star domatic number dSS(G). In particular, we determine the signed domatic number of some classes of graphs