On the Local Metric Dimension of Graphs

IF 0.5 Q4 COMPUTER SCIENCE, THEORY & METHODS

JOURNAL OF INTERCONNECTION NETWORKS Pub Date : 2024-01-10 DOI:10.1142/s0219265923500330

Chenxu Yang, Xingchao Deng, Jinxia Liang, Yuhu Liu

引用次数: 0

Abstract

Let [Formula: see text] be a graph. A set [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 characterize the graphs with [Formula: see text]. Next, we obtain the Nordhaus–Gaddum-type results for local metric dimension. Finally, the local metric dimension of several graph classes is given.

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论图形的局部度量维度

设[公式：见文本]是一个图。如果存在[公式：见文本]，使得任意[公式：见文本]的[公式：见文本]都是[公式：见文本]的局部解析集，那么集合[公式：见文本]就是[公式：见文本]的局部解析集。公式：见文本]的局部度量维度[公式：见文本]是[公式：见文本]所有局部解析集合的最小心数。在本文中，我们用[公式：见正文]来描述图的特征。接着，我们得到了关于局部度量维度的诺德豪斯-加登姆（Nordhaus-Gaddum）式结果。最后，我们给出了几类图的局部度量维度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

JOURNAL OF INTERCONNECTION NETWORKS COMPUTER SCIENCE, THEORY & METHODS-

自引率

14.30%

发文量

121

期刊介绍： The Journal of Interconnection Networks (JOIN) is an international scientific journal dedicated to advancing the state-of-the-art of interconnection networks. The journal addresses all aspects of interconnection networks including their theory, analysis, design, implementation and application, and corresponding issues of communication, computing and function arising from (or applied to) a variety of multifaceted networks. Interconnection problems occur at different levels in the hardware and software design of communicating entities in integrated circuits, multiprocessors, multicomputers, and communication networks as diverse as telephone systems, cable network systems, computer networks, mobile communication networks, satellite network systems, the Internet and biological systems.