Watching Systems in graphs: an extension of Identifying Codes
David Auger, Ir\`ene Charon, Olivier Hudry, Antoine Lobstein
TL;DR
This paper introduces watching systems in graphs, extending identifying codes, and explores their properties, bounds, specific cases like paths and cycles, and computational complexity.
Contribution
It generalizes the concept of identifying codes to watching systems, providing foundational properties, bounds, and complexity results.
Findings
Established basic properties of watching systems
Derived upper bounds on minimum size
Analyzed specific graph classes like paths and cycles
Abstract
We introduce the notion of watching systems in graphs, which is a generalization of that of identifying codes. We give some basic properties of watching systems, an upper bound on the minimum size of a watching system, and results on the graphs which achieve this bound; we also study the cases of the paths and cycles, and give complexity results.
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Taxonomy
TopicsCellular Automata and Applications · DNA and Biological Computing · Coding theory and cryptography