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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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
Online AccessGet full text
ISSN0973-8975
2454-7190
DOI10.26782/jmcms.2025.05.00005

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Abstract 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
AbstractList 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.
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
Author Batiha, Iqbal M.
Anakira, Nidal
Shehab, Mohammad
Mohamed, Basma
Odetatllah, Huda
Odeh, Mohammad
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SubjectTerms alternate snake graph
metric basis
metric dimension
Title SECURE METRIC DIMENSION OF ALTERNATE SNAKE GRAPHS
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