Private Out-Domination Number of Generalized de Bruijn Digraphs

Dominating sets are widely applied in the design and efficient use of computer networks. They can be used to decide the placement of limited resources, so that every node has access to the resource through neighbouring node. The most efficient solution is one that avoids duplication of access to the resources. This more restricted version of minimum dominating set is called an private dominating set. A vertex v in a digraph D is called a private out-neighbor of the vertex u in S (subset of V(D)) if u is the only element in the intersection of in-neighborhood set of v and S. A subset S of the vertex set V (D) of a digraph D is called a private out-dominating set of D if every vertex of V − S is a private out-neighbor of some vertex of S. The minimum cardinality of a private out-dominating set is called the private out-domination number. In this paper, we investigate the private out-domination number of generalized de Bruijn digraphs. We estabilsh the bounds of private out-domination number. Finally, we present exact values and sharp upperbounds of private out-domination number of some classes of generalized de Bruijn digraphs

Efficient total domination in digraphs

We generalize the concept of efficient total domination from graphs to digraphs. An efficiently total dominating set X of a digraph D is a vertex subset such that every vertex of D has exactly one predecessor in X . Not every digraph has an efficiently total dominating set. We study graphs that permit an orientation having such a set and give complexity results and characterizations concerning this question. Furthermore, we study the computational complexity of the (weighted) efficient total domination problem for several digraph classes. In particular we deal with most of the common generalizations of tournaments, like locally semicomplete and arc-locally semicomplete digraphs

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum