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
Authors | Manuel, Paul, Rajan, Bharati, Grigorious, Cyriac and Stephen, Sudeep |
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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. |
Keywords | Metric basis; Strong metric basis; Metric dimension; Strong metric dimension; Tetrahedral diamond lattice |
Year | 01 Jan 2015 |
Journal | Mathematics in Computer Science |
Journal citation | 9 (2), pp. 201-208 |
Publisher | Springer Basel AG |
ISSN | 1661-8270 |
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 scholarly | Research |
Page range | 201-208 |
Publisher's version | License All rights reserved File Access Level Controlled |
Output status | Published |
Publication dates | |
Online | 07 May 2015 |
Publication process dates | |
Accepted | 23 Mar 2015 |
Deposited | 21 May 2024 |
Additional information | © Springer Basel 2015 |
Place of publication | Switzerland |
https://acuresearchbank.acu.edu.au/item/907v0/on-the-strong-metric-dimension-of-tetrahedral-diamond-lattice
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