Abstract
Let G be a connected graph and W a set of vertices of G. If every vertex of G is determined by its distances to the vertices in W, then W is said to be a resolving set. The cardinality of a minimum resolving set is called the metric dimension of G. In this paper we determine the maximum number of vertices in a bipartite graph of given metric dimension and diameter. We also determine the minimum metric dimension of a bipartite graph of given maximum degree.
| Original language | English |
|---|---|
| Pages (from-to) | 487-498 |
| Number of pages | 12 |
| Journal | Discussiones Mathematicae - Graph Theory |
| Volume | 43 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2023 |
Keywords
- bipartite graph
- diameter
- maximum degree
- metric dimension
- resolving set
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics