Strongly Connected Dominating Set

Years and Authors of Summarized Original Work

• 2006; Du, Thai, Li, Liu, Zhu

• 2007: Park, Willson, Wang, Thai, Wu, Du

• 2009; Li, Du, Wan, Gao, Zhang, Wu

• 2012; Xu, Li

• 2014; Zhang, Wu, Wu, Li, Chen

Problem Definition

Let G = (V, E) be a directed graph. For an arc (u, v) ∈ E, u is said to dominate v, and v is said to absorb u. Vertex u is also called a dominator of v, and vertex v is called an absorber of u. A vertex set $D \subseteq V$ is a dominating set (DS) of G if every vertex in $V \setminus D$ has a dominator in D; it is an absorbing set (AS) of G if every vertex in $V \setminus D$ has an absorber in D. A directed graph G is strongly connected if for any pair of ordered vertices u, v ∈ V, there is a directed path in G from u to v. The “Minimum Strongly Connected Dominating and Absorbing Set” problem (MSCDAS) is to find a vertex set D such that D is both a dominating set and an absorbing set of G and the subgraph of G induced by D is strongly connected.

Disk graph is a geometric...