- Title
- On the strong metric dimension of tetrahedral diamond lattice
- Creator
- Manuel, Paul; Rajan, Bharati; Grigorious, Cyriac; Stephen, Sudeep
- Relation
- Mathematics in Computer Science Vol. 9, Issue 2, p. 201-208
- Publisher Link
- http://dx.doi.org/10.1007/s11786-015-0226-0
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2015
- Description
- 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.
- Subject
- metric basis; strong metric basis; metric dimension; strong metric dimension; tetrahedral diamond lattice
- Identifier
- http://hdl.handle.net/1959.13/1339545
- Identifier
- uon:28278
- Identifier
- ISSN:1661-8270
- Language
- eng
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