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Mathematics
Article . 2025 . Peer-reviewed
License: CC BY
Data sources: Crossref
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Mathematics
Article . 2025
Data sources: DOAJ
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An Upper Bound for the Eternal Roman Domination Number

Authors: Richard Brewster; Gary MacGillivray; Ethan Williams;

An Upper Bound for the Eternal Roman Domination Number

Abstract

Imagine using mobile guards to defend the vertices of a graph G from a sequence of attacks subject to the conditions that after each attack: (i) each guard either remains in place or moves to an adjacent vertex; (ii) the configuration of guards forms a Roman-dominating set; and (iii) there is at least one guard on each attacked vertex. We show that it is always possible to defend the vertices of a tree with n vertices using at most 5n6 guards and that this bound is tight.

Keywords

pursuit-evasion game, QA1-939, discrete-time graph process, Mathematics, domination

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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!
0
Average
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