Abstract
For a simple connected graph G=(V,E), an ordered set W⊆V, is called a resolving set of G if for every pair of two distinct vertices u and v, there is an element w in W such that d(u,w)≠d(v,w). A metric basis of G is a resolving set of G with minimum cardinality. The metric dimension of G is the cardinality of a metric basis and it is denoted by β(G). In this article, we determine the metric dimension of power of finite paths and characterize all metric bases for the same.
Original language | English |
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Article number | 2445 |
Number of pages | 13 |
Journal | Mathematics |
Volume | 10 |
Issue number | 14 |
DOIs | |
Publication status | Published - 13 Jul 2022 |
Keywords
- metric dimension
- graph
- code
- resolving set