On the Characterization of Maximal Planar Graphs with a Given Signed Cycle Domination Number

Let G =（V, E） be a simple graph. A function f : E → {+1,-1} is called a signed cycle domination function（SCDF） of G if ∑e∈E（C）f（e） ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γ'sc（G） = min{∑e∈Ef（e）| f is an SCDF of G}. This paper will characterize all maximal planar graphs G with order n ≥ 6 and γ'sc（G） = n.