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∈E f(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.