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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Eternal Domination Numbers of \(5 \times n\) Grid Graphs

Christopher M. van Bommel1, Martin F. van Bommel2
1Department of Mathematics and Statistics University of Victoria, Victoria, BC, V8W 2Y2, Canada
2Department of Mathematics, Statistics, and Computer Science St. Francis Xavier University, Antigonish, NS, B2G 2W5, Canada
  • Published: 31/05/2016

Abstract

Eternal domination of a graph requires the positioning of guards to protect against an infinitely long sequence of attacks where, in response to an attack, each guard can either remain in place or move to a neighbouring vertex, while keeping the graph dominated. This paper investigates the \( m \)-eternal domination numbers for \( 5 \times n \) grid graphs. The values, previously known for \( 1 \leq n \leq 5 \), are determined for \( 6 \leq n \leq 12 \), and lower and upper bounds derived for \( n > 12 \).

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Citation
Christopher M. van Bommel, Martin F. van Bommel. Eternal Domination Numbers of \(5 \times n\) Grid Graphs[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 097. 83-102. DOI: .