SECURE METRIC DIMENSION OF ALTERNATE SNAKE GRAPHS

We study the NP-hard problem of determining the secure metric dimension of graphs. A resolving set uniquely identifies each vertex by its distance vector to the set; the smallest is the metric basis, and its size is the metric dimension. A set is secure if each outside vertex can replace an inside o...

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Bibliographic Details
Published inJournal of mechanics of continua and mathematical sciences Vol. 20; no. 5; pp. 54 - 68
Main Authors Mohamed, Basma, Batiha, Iqbal M., Anakira, Nidal, Odeh, Mohammad, Shehab, Mohammad, Odetatllah, Huda
Format Journal Article
LanguageEnglish
Published Institute of Mechanics of Continua and Mathematical Sciences 01.05.2025
Subjects
alternate snake graph
metric basis
metric dimension
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Summary:We study the NP-hard problem of determining the secure metric dimension of graphs. A resolving set uniquely identifies each vertex by its distance vector to the set; the smallest is the metric basis, and its size is the metric dimension. A set is secure if each outside vertex can replace an inside one while preserving resolvability. Computing this parameter is NP-complete and has applications in routing, image processing, and network verification. This paper determines the secure metric dimension for alternate snake graphs, including k-polygonal, double, and triple alternate triangular snakes
ISSN:0973-8975
2454-7190
DOI:10.26782/jmcms.2025.05.00005