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...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Institute of Mechanics of Continua and Mathematical Sciences
2025-05-01
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| Series: | Journal of Mechanics of Continua and Mathematical Sciences |
| Subjects: | |
| Online Access: | https://jmcms.s3.amazonaws.com/wp-content/uploads/2025/05/14191738/jmcms-2505011-Secure-Metric-Dimension-Batiha.pdf |
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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. |
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| ISSN: | 0973-8975 2454-7190 |