Double Total Domination in Harary Graphs

TL;DR

This paper determines the double total domination number for Harary graphs, a specific class of graphs, providing insights into their dominating set properties.

Contribution

It introduces the exact calculation of the double total domination number specifically for Harary graphs, a new contribution to graph domination theory.

Findings

Exact formulas for double total domination number of Harary graphs

Extension of domination concepts to specific graph classes

Potential applications in network design and analysis

Abstract

Let $G$ be a graph with minimum degree at least 2. A set $D\subseteq V$ is a double total dominating set of $G$ if each vertex is adjacent to at least two vertices in $D$. The double total domination number $\gamma _{\times 2,t}(G)$ of $G$ is the minimum cardinality of a double total dominating set of $G$. In this paper, we will find double total domination number of Harary graphs.