Certified domination
Magda Dettlaff, Magdalena Lema\'nska, Jerzy Topp, Rados{\l}aw Ziemann,, Pawe{\l} \.Zyli\'nski

TL;DR
This paper introduces the concept of certified domination in graphs, modeling a security scenario with officials and witnesses, and explores its properties, bounds, and computational complexity.
Contribution
It defines the certified domination number, provides exact values for certain graphs, bounds for general graphs, and proves the NP-completeness of the decision problem.
Findings
Exact certified domination numbers for specific graph classes
Upper bounds for arbitrary graphs
NP-completeness of the certified domination problem
Abstract
Imagine that we are given a set of officials and a set of civils. For each civil , there must be an official that can serve , and whenever any such is serving , there must also be another civil that observes , that is, may act as a kind of witness, to avoid any abuse from . What is the minimum number of officials to guarantee such a service, assuming a given social network? In this paper, we introduce the concept of certified domination that perfectly models the aforementioned problem. Specifically, a dominating set of a graph is said to be certified if every vertex in has either zero or at least two neighbours in . The cardinality of a minimum certified dominating set in is called the certified domination number of . Herein, we present the exact values of the certified domination…
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Taxonomy
TopicsAdvanced Graph Theory Research · Game Theory and Voting Systems · Complexity and Algorithms in Graphs
