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Dihedral group as generalized conjugacy class graph and its relevant matrices


Citation

Che Kamaruzaman, Siti Nur Shafila and Nawawi @ Mohamed Nawawi, Athirah (2021) Dihedral group as generalized conjugacy class graph and its relevant matrices. Advances in Mathematics: Scientific Journal, 10 (1). pp. 59-81. ISSN 1857-8365; ESSN: 1857-8438

Abstract

In this paper, the generalized conjugacy class graph for dihedral groupof order 2n is constructed to show the relation between the orbits and their cardinalities. The orbits of the set denoted by Ω must be computed first by using conjugation action. The elements in each orbit are all pairs of commuting elements in the form of (a, b) where a and b are elements of the dihedral group and the lowest common multiple of the order of the elements has to be two. Also here, some relevant matrices named as adjacency, incident and Laplacian matrices that can represent the graph are also constructed. Eigenvalues from those matrices are computed to give information on graph energies either energy, denoted by ε(ΓG) or Laplacian energy, denoted by LE(ΓG). Interestingly, we have found that the values for both ε(ΓG) and LE(ΓG) are equal.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
DOI Number: https://doi.org/10.37418/amsj.10.1.7
Publisher: Union of Researchers of Macedonia
Keywords: Dihedral group; Laplacian matrix; Incidence matrix; Adjacency matrix; Generalized conjugacy class graph; Graph energy
Depositing User: Ms. Nuraida Ibrahim
Date Deposited: 01 Dec 2022 08:26
Last Modified: 01 Dec 2022 08:26
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=https://doi.org/10.37418/amsj.10.1.7
URI: http://psasir.upm.edu.my/id/eprint/96743
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