Some Upper Bounds for Signed Star Domination Number of Graphs

Let G be a graph with the 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 ofG if ∑ e∈EG(v) f(e) ≥ 1, for every v ∈ V (G), where EG(v) = {uv ∈ E(G) |u ∈ V (G)}. The minimum of the values of ∑ e∈E(G) f(e), taken over all signed star dominating functions f on G is called the signed star domination number of G and is denoted by γss(G). In this paper we show that if G is a connected graph of order n containing a 2-factor and G ̸= K5, then γss(G) ≤ 7n 6 . Among other results it is shown that if G is connected and α(G) ≤ 2, then γss(G) ≤ n+ 1, where α(G) is the independence number of G.