Volume 10, Issue 11 (November 2023), Pages: 176-183

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 Original Research Paper

Conjugacy classes and conjugate graph of a K-metacyclic group

 Author(s): 

 Yangertola Yangertola *, Kuntala Patra

 Affiliation(s):

 Department of Mathematics, Gauhati University, Guwahati, Assam, India

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0009-0008-4199-3383

 Digital Object Identifier (DOI)

 https://doi.org/10.21833/ijaas.2023.11.022

 Abstract

The relationship between algebraic structures and graphs has become an interesting topic of research nowadays. In this paper, we have considered the conjugate graph related to the conjugacy relation of a group. The vertices of the said graph are the noncentral elements of the group, and two vertices are adjacent if they are conjugate. For this particular study, we focused on the conjugate graph of a K-metacyclic group of order p(p-1). We first determine the conjugacy classes of this group and then obtain its conjugate graph. Various graph properties such as planarity, line graph, complement graph, clique number, dominating number, spectrum, and Laplacian are also studied in this paper.

 © 2023 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords

 K-metacyclic group, Conjugacy class, Conjugate graph

 Article history

 Received 8 July 2023, Received in revised form 2 November 2023, Accepted 5 November 2023

 Acknowledgment 

The authors would like to thank the referees for their valuable comments. Further, the first author is thankful to the Council of Scientific and Industrial Research for the JRF fellowship, UGC-Ref. No.:1102/(CSIR-UGC NET DEC.2018).

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Yangertola Y and Patra K (2023). Conjugacy classes and conjugate graph of a K-metacyclic group. International Journal of Advanced and Applied Sciences, 10(11): 176-183

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 Figures

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