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 ..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 ..sc(G) = n.