On signed cycle domination in graphs

AbstractLet G=(V,E) be a graph, a function f:E→{−1,1} is said to be an signed cycle dominating function (SCDF) of G if ∑e∈E(C)f(e)≥1 holds for any induced cycle C of G. The signed cycle domination number of G is defined as γsc′(G)=min{∑e∈E(G)f(e)∣f is an SCDF of G}. In this paper, we obtain bounds on γsc′(G), characterize all connected graphs G with γsc′(G)=|E(G)|−2, and determine the exact value of γsc′(G) for some special classes of graphs G. In addition, we pose some open problems and conjectures