On the Strong Metric Dimension of Tetrahedral Diamond Lattice

Journal article

Manuel, Paul, Rajan, Bharati, Grigorious, Cyriac and Stephen, Sudeep. (2015). On the Strong Metric Dimension of Tetrahedral Diamond Lattice. Mathematics in Computer Science. 9(2), pp. 201-208. https://doi.org/10.1007/s11786-015-0226-0
AuthorsManuel, Paul, Rajan, Bharati, Grigorious, Cyriac and Stephen, Sudeep
Abstract

A resolving set is a set W of vertices of a connected graph G(V, E) such that for every pair of vertices u, v of G, there exists a vertex w ∈ W with the condition that the length of a shortest path from u to w is different from the length of a shortest path from v to w. A resolving set of minimum cardinality of G is called a metric basis. Metric dimension is the cardinality of a metric basis. A pair of vertices u, v is said to be strongly resolved by a vertex s, if there exists at least one shortest path from s to u passing through v, or a shortest path from s to v passing through u. A set W ⊆ V, is said to be a strong resolving set if for all pairs u, v /∈ W, there exists some element s ∈ W such that s strongly resolves the pair u, v. A strong resolving set of minimum cardinality is called a strong metric basis. The cardinality of a strong metric basis for G is called the strong metric dimension of G. The strong metric dimension (metric dimension) problem is to find a strong metric basis (metric basis) in the graph. In this paper, we solve the strong metric dimension and the metric dimension problems for the graph of tetrahedral diamond lattice.

KeywordsMetric basis; Strong metric basis; Metric dimension; Strong metric dimension; Tetrahedral diamond lattice
Year01 Jan 2015
JournalMathematics in Computer Science
Journal citation9 (2), pp. 201-208
PublisherSpringer Basel AG
ISSN1661-8270
Digital Object Identifier (DOI)https://doi.org/10.1007/s11786-015-0226-0
Web address (URL)https://link.springer.com/article/10.1007/s11786-015-0226-0
Research or scholarlyResearch
Page range201-208
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All rights reserved
File Access Level
Controlled
Output statusPublished
Publication dates
Online07 May 2015
Publication process dates
Accepted23 Mar 2015
Deposited21 May 2024
Additional information

© Springer Basel 2015

Place of publicationSwitzerland
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