Independent Domination in Directed Graphs

TL;DR

This paper introduces the concept of independent domination in directed graphs, exploring its properties, existence, and uniqueness across various graph classes, and providing specific parameters for special cases.

Contribution

It is the first study to systematically analyze independent domination in directed graphs, establishing foundational theorems and parameters for multiple graph families.

Findings

Independent dominating set in an orientation is also valid in the underlying graph.

Existence and uniqueness theorems are proven for several classes of digraphs.

The idomatic number is determined for specific subclasses of digraphs.

Abstract

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, trees, DAGs, cycles, and bipartite graphs. We also provide the idomatic number for special cases of some of these families of digraphs.