Graphs with equal domination and certified domination numbers
Magda Dettlaff, Magdalena Lema\'nska, Mateusz Miotk, Jerzy Topp,, Rados{\l}aw Ziemann, Pawe{\l} \.Zyli\'nski

TL;DR
This paper investigates the relationships between various domination parameters in graphs, including domination, upper domination, certified domination, and upper certified domination numbers, providing new insights into their interconnections.
Contribution
It introduces and analyzes the relationships among four domination parameters, including the newly defined certified domination and upper certified domination numbers.
Findings
Established bounds between domination and certified domination numbers.
Characterized graphs where these parameters are equal.
Provided new inequalities relating the different domination numbers.
Abstract
A set of vertices of a graph is a dominating set of if every vertex in is adjacent to at least one vertex in . The domination number (upper domination number, respectively) of a graph , denoted by (, respectively), is the cardinality of a smallest (largest minimal, respectively) dominating set of . A subset is called a certified dominating set of if is a dominating set of and every vertex in has either zero or at least two neighbors in . The cardinality of a~smallest (largest minimal, respectively) certified dominating set of is called the certified upper certified, respectively domination number of and is denoted by (, respectively). In this paper relations between domination, upper domination, certified domination and upper certified domination…
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Complexity and Algorithms in Graphs
