Dihedral group as generalized conjugacy class graph and its relevant matrices
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 commut...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Union of Researchers of Macedonia
2021
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/96743/ http://psasir.upm.edu.my/id/eprint/96743/1/ABSTRACT.pdf |
| _version_ | 1848862434397257728 |
|---|---|
| author | Che Kamaruzaman, Siti Nur Shafila Nawawi @ Mohamed Nawawi, Athirah |
| author_facet | Che Kamaruzaman, Siti Nur Shafila Nawawi @ Mohamed Nawawi, Athirah |
| author_sort | Che Kamaruzaman, Siti Nur Shafila |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T13:16:58Z |
| format | Article |
| id | upm-96743 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T13:16:58Z |
| publishDate | 2021 |
| publisher | Union of Researchers of Macedonia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-967432022-12-01T08:26:06Z http://psasir.upm.edu.my/id/eprint/96743/ Dihedral group as generalized conjugacy class graph and its relevant matrices Che Kamaruzaman, Siti Nur Shafila Nawawi @ Mohamed Nawawi, Athirah 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. Union of Researchers of Macedonia 2021 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/96743/1/ABSTRACT.pdf 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 https://www.research-publication.com/amsj/all-issues/vol-10/iss-01/index.html 10.37418/amsj.10.1.7 |
| spellingShingle | Che Kamaruzaman, Siti Nur Shafila Nawawi @ Mohamed Nawawi, Athirah Dihedral group as generalized conjugacy class graph and its relevant matrices |
| title | Dihedral group as generalized conjugacy class graph and its relevant matrices |
| title_full | Dihedral group as generalized conjugacy class graph and its relevant matrices |
| title_fullStr | Dihedral group as generalized conjugacy class graph and its relevant matrices |
| title_full_unstemmed | Dihedral group as generalized conjugacy class graph and its relevant matrices |
| title_short | Dihedral group as generalized conjugacy class graph and its relevant matrices |
| title_sort | dihedral group as generalized conjugacy class graph and its relevant matrices |
| url | http://psasir.upm.edu.my/id/eprint/96743/ http://psasir.upm.edu.my/id/eprint/96743/ http://psasir.upm.edu.my/id/eprint/96743/ http://psasir.upm.edu.my/id/eprint/96743/1/ABSTRACT.pdf |