关于线形图的局部度量维数

IF 0.5 Q4 COMPUTER SCIENCE, THEORY & METHODS JOURNAL OF INTERCONNECTION NETWORKS Pub Date : 2023-10-31 DOI:10.1142/s0219265923500263

Chenxu Yang, Xingchao Deng, Wen Li

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引用次数: 0

摘要

设[公式:见文本]为图形。对于任何[公式:见文]，如果存在[公式:见文]使得[公式:见文]，我们说[公式:见文]消解[公式:见文]。如果存在[公式:见文本]使得[公式:见文本]对于任何[公式:见文本]，[公式:见文本]的顶点集[公式:见文本]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]的所有局部解析集的最小基数。本文研究了[公式:见文]与[公式:见文]之间的关系。此外，我们构造了一个图[公式:见文]，使得[公式:见文]和[公式:见文]。最后，我们研究了几种特殊线形图的局部度量维数。

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On the Local Metric Dimension of Line Graphs

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.

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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.