On the Local Metric Dimension of Line Graphs-Reference-Cited by-同舟云学术

On the Local Metric Dimension of Line Graphs

Published:2023-10-31 Issue: Volume: Page:
ISSN:0219-2659
Container-title:Journal of Interconnection Networks
language:en
Short-container-title:J. Inter. Net.

Author:

Yang Chenxu¹^ORCID,Deng Xingchao²^ORCID,Li Wen³^ORCID

Affiliation:

1. School of Computer, Qinghai Normal University, Xining, Qinghai 810008, P. R. China

2. School of Mathematical Science, Tianjin Normal University, Tianjin 300387, P. R. China

3. School of Mathematics and Statistics, Qinghai Minzu University, Xining, Qinghai 810008, P. R. China

Abstract

Let [Formula: see text] be a graph. For any [Formula: see text], if there exists [Formula: see text] such that [Formula: see text], we say that [Formula: see text] resolving [Formula: see text]. A set [Formula: see text] of vertices in [Formula: see text] is a local resolving set of [Formula: see text] if there exists [Formula: see text] such that [Formula: see text] for any [Formula: see text]. The local metric dimension [Formula: see text] of [Formula: see text] is the minimum cardinality of all the local resolving sets of [Formula: see text]. In this paper, we study the relation between [Formula: see text] and [Formula: see text]. Furthermore, we construct a graph [Formula: see text] such that [Formula: see text] and [Formula: see text]. Finally, we investigate the local metric dimension of several special line graphs.

Funder

National Science Foundation of China

Qinghai Key Laboratory of Internet of Things Project

Tianjin Normal University Research Innovation Project for Postgraduate Students, China

Publisher

World Scientific Pub Co Pte Ltd

Subject

Computer Networks and Communications

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219265923500263

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Secure metric dimension of new classes of graphs;Mathematical Models in Engineering;2024-07-15