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https://doi.org/10.2139/ssrn.4...
Article . 2023 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2023
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
DBLP
Preprint . 2023
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Computing M-Eternal Domination Number of Cactus Graphs in Linear Time

Authors: Václav Blazej; Jan Matyás Kristan; Tomás Valla;

Computing M-Eternal Domination Number of Cactus Graphs in Linear Time

Abstract

In m-eternal domination attacker and defender play on a graph. Initially, the defender places guards on vertices. In each round, the attacker chooses a vertex to attack. Then, the defender can move each guard to a neighboring vertex and must move a guard to the attacked vertex. The m-eternal domination number is the minimum number of guards such that the graph can be defended indefinitely. In this paper, we study the m-eternal domination number of cactus graphs. We consider two variants of the m-eternal domination number: one allows multiple guards to occupy a single vertex, the second variant requires the guards to occupy distinct vertices. We develop several tools for obtaining lower and upper bounds on these problems and we use them to obtain an algorithm which computes the minimum number of required guards of cactus graphs for both variants of the problem.

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Keywords

FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Computer Science - Data Structures and Algorithms, Data Structures and Algorithms (cs.DS), Computer Science - Discrete Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green