On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs

被引：12
作者：
Hayat, Sakander [1 ]
Khan, Asad [2 ]
Zhong, Yubin [1 ]
机构：
[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Peoples R China
[2] Guangzhou Univ, Sch Comp Sci & Cyber Engn, Guangzhou 510006, Peoples R China
来源：
MATHEMATICS | 2022年 / 10卷 / 11期
关键词：
graph; resolving set; dominating set; metric-dominating set; complete multipartite graph; MIXED METRIC DIMENSION; NUMBER; PRODUCT; CODES; SETS; P(N;
D O I：
10.3390/math10111815
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Graphs of order n with fault-tolerant metric dimension n have recently been characterized.This paper points out an error in the proof of this characterization. We show that the complete multipartite graphs also have the fault-tolerant metric dimension n, which provides an infinite family of counterexamples to the characterization. Furthermore, we find exact values of the metric, edge metric, mixed-metric dimensions, the domination number, locating-dominating number, and metric-locating-dominating number for the complete multipartite graphs. These results generalize various results in the literature from complete bipartite to complete multipartite graphs.
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页数：16
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