The edge metric dimension of the generalized Petersen graph $P(n,3)$ is 4
Combinatorics
2020-06-12 v3
Abstract
It is known that the problem of computing the edge dimension of a graph is NP-hard, and that the edge dimension of any generalized Petersen graph is at least 3. We prove that the graph has edge dimension 4 for , by showing semi-combinatorially the nonexistence of an edge resolving set of order 3 and by constructing explicitly an edge resolving set of order 4.
Cite
@article{arxiv.2005.08038,
title = {The edge metric dimension of the generalized Petersen graph $P(n,3)$ is 4},
author = {David G. L. Wang and Monica M. Y. Wang and Shiqiang Zhang},
journal= {arXiv preprint arXiv:2005.08038},
year = {2020}
}
Comments
28 pages, 1 figure, 21 tables