English

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 P(n,k)P(n,k) is at least 3. We prove that the graph P(n,3)P(n,3) has edge dimension 4 for n11n\ge 11, 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.

Keywords

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