On Roman, Global and Restrained Domination in Graphs
A. Poghosyan, V. Zverovich
TL;DR
This paper introduces new upper bounds for various domination parameters in graphs, proves their asymptotic optimality, and explores the relationships between restrained and standard domination numbers.
Contribution
It provides novel upper bounds for global, Roman, restrained, and total restrained domination numbers, with asymptotic optimality proofs and insights into their equality with standard domination numbers.
Findings
New upper bounds for domination parameters
Asymptotic optimality of these bounds
Equality of restrained and standard domination numbers in almost all graphs
Abstract
In this paper, we present new upper bounds for the global domination and Roman domination numbers and also prove that these results are asymptotically best possible. Moreover, we give upper bounds for the restrained domination and total restrained domination numbers for large classes of graphs, and show that, for almost all graphs, the restrained domination number is equal to the domination number, and the total restrained domination number is equal to the total domination number. A number of open problems are posed.
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Taxonomy
TopicsAdvanced Graph Theory Research · Game Theory and Applications