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The Strong Metric Dimension of Some Generalized Petersen Graphs
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kratica, Jozef Kovacevic-Vujcic, Vera Cangalovic, Mirjana |
| Copyright Year | 2017 |
| Abstract | The strong metric dimension problem was introduced by Sebo and Tannier [13]. This problem is defined in the following way. Given a simple connected undirected graph G = (V ,E), where V = {1, 2, . . . , n}, |E| = m and d(u, v) denotes the distance between vertices u and v, i.e. the length of a shortest u − v path. A vertex w strongly resolves two vertices u and v if u belongs to a shortest v−w path or v belongs to a shortest u−w path. A vertex set S of G is a strong resolving set of G if every two distinct vertices of G are strongly resolved by some vertex of S. A strong metric basis of G is a strong resolving set of the minimum cardinality. The strong metric dimension of G, denoted by sdim(G), is defined as the cardinality of a strong metric basis. Now, the strong metric dimension problem is defined as the problem of finding the strong metric dimension of a graph G. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://pefmath.etf.rs/vol11num1/AADM-Vol11-No1-1-10.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Cardinality Emoticon Graph - visual representation Julius Petersen Metric dimension (graph theory) Short Undirected Graph Vertex (geometry) Vertex (graph theory) |
| Content Type | Text |
| Resource Type | Article |
