On the Geodesic Identification of Vertices in Convex Plane Graphs
A shortest path between two vertices u and v in a connected graph G is a u−v geodesic. A vertex w of G performs the geodesic identification for the vertices in a pair u,v if either v belongs to a u−w geodesic or u belongs to a v−w geodesic. The minimum number of vertices performing the geodesic iden...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2020-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2020/7483291 |
| Summary: | A shortest path between two vertices u and v in a connected graph G is a u−v geodesic. A vertex w of G performs the geodesic identification for the vertices in a pair u,v if either v belongs to a u−w geodesic or u belongs to a v−w geodesic. The minimum number of vertices performing the geodesic identification for each pair of vertices in G is called the strong metric dimension of G. In this paper, we solve the strong metric dimension problem for three convex plane graphs by performing the geodesic identification of their vertices. |
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| ISSN: | 1563-5147 |