Signed Cycle Domination Numbers of Digraphs

Abstract

The concept of signed cycle domination number of graphs, introduced by B. Xu [B. Xu, On signed cycle domination in graphs, Discrete Math. \(309 (2009)1007-1012]\), is extended to digraphs, denoted by \(\gamma’_{sc}(D)\) for a digraph \(D\). We establish bounds on \(\gamma_s(D)\), characterize all digraphs \(D\) with \(\gamma’_{sc}(D) = |A(D)|-2\), and determine the exact value of \(\gamma’_{sc}(D)\) for specific classes of digraphs \(D\). Furthermore, we define the parameter \(g'(m,n) = \min\{\gamma’_{sc}(D) \mid D \text{ is a digraph with } |V(D)| = n \text{ and } |A(D)| = m\}\) and obtain its value for all integers \(n\) and \(m\) satisfying \(0 \leq m \leq n(n-1)\).