New resolvability parameters of graphs
| Autor: | Stephen T. Hedetniemi, Renu C. Laskar, Henry Martyn Mulder |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | AKCE International Journal of Graphs and Combinatorics, Vol 17, Iss 3, Pp 1028-1038 (2020) |
| Druh dokumentu: | article |
| ISSN: | 0972-8600 2543-3474 |
| DOI: | 10.1016/j.akcej.2019.12.021 |
| Popis: | In this paper we introduce two concepts related to resolvability and the metric dimension of graphs. The kth dimension of a graph G is the maximum cardinality of a subset of vertices of G that is resolved by a set S of order k. Some first results are obtained. A pair of vertices u, v is totally resolved by a third vertex x if A total resolving set in G is a set S such that each pair of vertices of G is totally resolved be a vertex in S. The total metric dimension of a graph is the minimum cardinality of a total resolving set. We determine the total metric dimension of paths, cycles, and grids, and of the 3-cube, and the Petersen graph. |
| Databáze: | Directory of Open Access Journals |
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