Abstract
Let be a connected graph of order n. Two vertices p and q in V are said to resolve by a vertex if . An ordered subset of vertices in Γ is said to be resolving set if for every pair p, q of distinct vertices in V, we have , where is the l-code/metric coordinate representation of the vertex a with respect to the set F. The resolving set for Γ with minimum cardinality is known as metric basis for the graph Γ and the cardinality of metric basis is called as metric dimension of Γ. In this work, we demonstrate that for two families of convex polytopes which are closely linked, the metric dimension is constant.
Authors' contributions
The first draft was written by Malkesh Singh and Vijay Kumar Bhat. Figures have been prepared by Malkesh Singh and Tables have been prepared by Vijay Kumar Bhat. Both the authors reviewed the final draft.
Funding
No specific funding was received for this work.
Data Availability
No data or software were used to support the findings of this study, and no data or software has been generated.
Acknowledgments
The authors would like to express their sincere thanks to the anonymous reviewers for their comments and suggestions that lead to improvements and the present shape of the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).