On the metric dimension of circulant and Harary graphs
A metric generator is a set W of vertices of a 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. In this case the vertex w is said to res...
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| Veröffentlicht in: | Applied mathematics and computation 2014-12, Vol.248, p.47-54 |
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| creator | Grigorious, Cyriac Manuel, Paul Miller, Mirka Rajan, Bharati Stephen, Sudeep |
| description | A metric generator is a set W of vertices of a 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. In this case the vertex w is said to resolve or distinguish the vertices u and v. The minimum cardinality of a metric generator for G is called the metric dimension. The metric dimension problem is to find a minimum metric generator in a graph G. In this paper, we make a significant advance on the metric dimension problem for circulant graphs C(n,±{1,2,…,j}),1⩽j⩽⌊n/2⌋,n⩾3, and for Harary graphs. |
| doi_str_mv | 10.1016/j.amc.2014.09.045 |
| format | Article |
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| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Circulant graphs Computation Generators Graphs Harary graphs Mathematical models Metric basis Metric dimension Shortest-path problems |
| title | On the metric dimension of circulant and Harary graphs |
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