A note on double domination in graphs

TL;DR

This paper improves existing results on double domination in graphs, a topic within the broader study of multiple domination, by building upon recent research and techniques discussed in a comprehensive book on graph domination.

Contribution

It provides enhancements to known results on double domination, refining the understanding of this specific graph domination parameter.

Findings

Improved bounds or results on double domination in graphs.

Enhanced techniques for analyzing double domination.

Refined theoretical understanding of double domination properties.

Abstract

Recently, Haynes, Hedetniemi and Henning published the book Topics in Domination in Graphs, which comprises 16 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. One of these contributions is the chapter Multiple Domination, by Hansberg and Volkmann, where they put into context all relevant research results on multiple domination that have been found up to 2020. In this note, we show how to improve some results on double domination that are included in the book.