Results 221 to 230 of about 170,996 (244)

Eternal and Secure Domination in Graphs

open access: yesDevelopments in Mathematics, 2020
Mobile guards on the vertices of a graph are used to defend it against attacks that occur in sequence on its vertices. Various models for this problem have been proposed. In this chapter, we describe a number of these models with particular attention to two general cases (i) when the attack sequence is infinitely long and the guards must induce a ...
C M Mynhardt, William F Klostermeyer
exaly   +4 more sources

A note on the eternal dominating set problem

International Journal of Game Theory, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stephen Finbow   +2 more
exaly   +2 more sources

Eternal Total Domination in Graphs.

open access: yesArs Comb., 2012
Eternal domination of a graph requires the vertices of the graph to be protected, against infinitely long sequences of attacks, by guards located at vertices, with the requirement that the configuration of guards induces a dominating set at all times. We study some variations of this concept in which the configuration of guards induce total dominating ...
Klostermeyer, William F.   +1 more
core   +3 more sources

Dynamic dominating sets: the eviction model for eternal domination

open access: yes, 2016
In a graph \(G = (V,E)\), a dominating set \(D\) is a subset of the vertices \(V\) such that every vertex is either in \(D\) or adjacent to one. Applications of dominating sets include communications, distributed computing and security. For instance, each node in the graph represents a strategic site that needs protection, and two nodes are connected ...
Klostermeyer, William F.   +2 more
core   +3 more sources

Trees with large m-eternal domination number

open access: yesDiscrete Applied Mathematics, 2016
Mobile guards on the vertices of a graph are used to defend the graph against an infinite sequence of attacks on vertices. A guard must move from a neighboring vertex to an attacked vertex (we assume attacks happen only at vertices containing no guard ...
Michael Henning, William F Klostermeyer
exaly   +2 more sources

Eternal paired domination in graphs

Discrete Mathematics, Algorithms and Applications
Eternal dominationof a graph requires the vertices of the graph to be protected, against infinitely long sequences of attacks, by guards located at vertices (at most one guard at each vertex), with the requirement that the configuration of guards induces a dominating set at all times.
D. Yokesh   +2 more
openaire   +1 more source

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