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

Sakander Hayat, Asad Khan and Yubin Zhong
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Sakander Hayat: School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
Asad Khan: School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China
Yubin Zhong: School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China

Mathematics, 2022, vol. 10, issue 11, 1-16

Abstract: 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.

Keywords: graph; resolving set; dominating set; metric-dominating set; complete multipartite graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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