Foolproof eternal domination in the all-guards move model

Document Type

Article

Publication Date

8-1-2012

Abstract

The eternal domination problem requires a graph be protected against an infinitely long sequence of attacks at vertices, by guards located at vertices, with the requirement that the configuration of guards induces a dominating set at all times. An attack is defended by sending a guard from a neighboring vertex to the attacked vertex. We allow all guards to move to neighboring vertices in response to an attack, but allow the attacked vertex to choose which neighboring guard moves to the attacked vertex. This is the all-guards move version of the "foolproof" eternal domination problem that has been previously studied. We present some results and conjectures on this problem. © 2012 Versita Warsaw and Springer-Verlag Wien.

Publication Title

Mathematica Slovaca

Volume

62

Issue

4

First Page

595

Last Page

610

Digital Object Identifier (DOI)

10.2478/s12175-012-0033-x

ISSN

01399918

E-ISSN

13372211

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