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arXiv · 2306.12583

On Error-detecting Open-locating-dominating sets

Devin Jean·Suk Seo
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Abstract

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.

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Devin Jean, Suk Seo. 2023-06-21. On Error-detecting Open-locating-dominating sets. https://arxiv.org/abs/2306.12583

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