On Error-detecting Open-locating-dominating sets

An open-dominating set S for a graph G is a subset of vertices where every vertex has a neighbor in S. An open-locating-dominating set S for a graph G is an open-dominating set such that each pair of distinct vertices in G have distinct set of open-neighbors in S. We consider a type of a fault-toler...

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Bibliographic Details
Published inarXiv.org
Main Authors Devin, Jean, Seo, Suk
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.06.2023
Subjects
Apexes
Error detection
Fault tolerance
Graph theory
Graphs
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Summary:An open-dominating set S for a graph G is a subset of vertices where every vertex has a neighbor in S. An open-locating-dominating set S for a graph G is an open-dominating set such that each pair of distinct vertices in G have distinct set of open-neighbors in S. We consider a type of a fault-tolerant open-locating dominating set called error-detecting open-locating-dominating sets. We present more results on the topic including its NP-completeness proof, extremal graphs, and a characterization of cubic graphs that permit an error-detecting open-locating-dominating set.
ISSN:2331-8422