Cototal Litact Domination in Graphs

Abstract

Introduction: In the realm of graph theory, the study of domination has been a fundamental pursuit, exploring the notion of how certain vertices in a graph control or influences others. One such variant is cototal domination, which extends the concept of domination to consider sets of vertices that together control the entire graph. In this paper, we delve into the intriguing interplay of cototal domination within litact graphs.

Objectives: This work's primary goal is to ascertain the new domination parameter known as cototal domination on a litact graph.

Motivation

The exploration of cototal domination within litact graphs arises from the intersection of two intriguing areas of graph theory. Understanding how cototal domination manifests within litact graphs not only contributes to the theoretical foundation of graph domination but also unveils practical implications for network design, fault tolerance, and optimization.

Results: Several results on cototal domination on a litact graph are obtained in the present study, both in terms of different graph  parameters (vertices, edges, diameter, maximum degree, and many more) and domination parameters (connected domination, total domination, edge domination, and many more). A few fundamental definitions, findings, and the ideas of several dominations parameters have been used in this.

The current study aims to determine some relations between cototal on a litact graph and graph s different parameters, and domination parameters. Furthermore, results comparable to Nordhaus-Gaddum's were also established.

Summary of Findings

We have established the formal definitions and properties of cototal domination and litact graphs, laying the groundwork for our analysis. Our computational exploration has revealed the complexity of cototal domination in litact graphs and highlighted the challenges associated with determining cototal domination sets efficiently.

Conclusion

In conclusion, our exploration of cototal domination in litact graphs has shed light on the intricate dynamics of graph control within this unique class of graphs. Through our investigation, we have achieved several key insights and contributions.