Fault-Tolerant Metric Dimension of Barycentric Subdivision of Cayley Graphs

Metric dimension and fault-tolerant metric dimension of any graph G is subject to size of resolving set. It has become more important in modern GPS and sensors based world as resolving set ensures that in case of semi outage system is still scalable using redundant interfaces. Metric dimension of se...

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Published inKragujevac Journal of Mathematics Vol. 48; no. 3; pp. 433 - 439
Main Authors AHMAD, ALI, ASIM, MUHAMMAD A., BAČA, MARTIN
Format Journal Article
LanguageEnglish
Published 2024
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ISSN1450-9628
2406-3045
2406-3045
DOI10.46793/KgJMat2403.433A

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Summary:Metric dimension and fault-tolerant metric dimension of any graph G is subject to size of resolving set. It has become more important in modern GPS and sensors based world as resolving set ensures that in case of semi outage system is still scalable using redundant interfaces. Metric dimension of several interesting classes of graphs have been investigated like Cayley digraphs, Cartesian product of graphs, wheel graphs, convex polytopes and certain networks for categorical product of graphs. In this paper we used the phenomena of barycentric subdivision of graph and proved that fault-tolerant metric dimension of barycentric subdivision of Cayley graph is constant.
ISSN:1450-9628
2406-3045
2406-3045
DOI:10.46793/KgJMat2403.433A