Secure Domination in Digraphs

TL;DR

This paper extends the concept of secure dominating sets from undirected graphs to directed graphs (digraphs) in four different ways, exploring their properties and applications.

Contribution

It introduces four new definitions of secure domination in digraphs and provides initial theoretical results for each, broadening the understanding of domination in directed networks.

Findings

Four new secure domination concepts for digraphs introduced

Theoretical properties of each secure domination variant established

Potential applications in network security and control identified

Abstract

Given a graph G = (V,E), a subset S of V is dominating if for every v in V - S there exists u in S such that uv is in E. A dominating subset S of V is secure if for every v in V - S there exists u in S such that (S - {u}) U {v} is dominating. In this work we extend the concept of secure dominating set to digraphs in four different ways, all of them with interesting applications, and prove some results regarding each of them.