Degree-based energies of commuting graph for dihedral groups
Commuting graph for a finite group G, denoted by ΓG, with its set of vertices G\Z(G), where Z(G) is the center of G, is a graph with vp,vq ∈ G\Z(G), vp ≠ vq, are adjacent whenever vpvq = vq vp . In recent years, there has been significant research into the energy of graphs, particularly focusing on...
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| Format: | Article |
| Language: | English |
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Lviv Polytechnic National University
2025
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| Online Access: | http://psasir.upm.edu.my/id/eprint/121047/ http://psasir.upm.edu.my/id/eprint/121047/1/121047.pdf |
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| author | Romdhini, Mamika Ujianita Nawawi, Athirah |
| author_facet | Romdhini, Mamika Ujianita Nawawi, Athirah |
| author_sort | Romdhini, Mamika Ujianita |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Commuting graph for a finite group G, denoted by ΓG, with its set of vertices G\Z(G), where Z(G) is the center of G, is a graph with vp,vq ∈ G\Z(G), vp ≠ vq, are adjacent whenever vpvq = vq vp . In recent years, there has been significant research into the energy of graphs, particularly focusing on matrices associated with the degree of vertices. Therefore, motivated by that, our study elaborates on the energy of ΓG for dihedral groups of order 2n, D2n, concerning some graph matrices related to the degree of elements of D2n\Z(D2n) and examine the correlation between those energies. The matrices involved are known as geometric-arithmetic, symmetric division deg, degree exponent, inverse sum indeg and Sombor matrices. Based on these five matrices, it is found that the lowest graph energy is the geometric-arithmetic energy of ΓG whilst the highest is the degree exponent energy. Furthermore, the geometric-arithmetic, symmetric division deg, and degree exponent energies are always positive even integers. In contrast, the inverse sum indeg energy is a positive integer that can be either even or odd. Meanwhile, the Sombor energy is never an odd integer. |
| first_indexed | 2025-11-15T14:49:54Z |
| format | Article |
| id | upm-121047 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:49:54Z |
| publishDate | 2025 |
| publisher | Lviv Polytechnic National University |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1210472025-10-23T02:36:41Z http://psasir.upm.edu.my/id/eprint/121047/ Degree-based energies of commuting graph for dihedral groups Romdhini, Mamika Ujianita Nawawi, Athirah Commuting graph for a finite group G, denoted by ΓG, with its set of vertices G\Z(G), where Z(G) is the center of G, is a graph with vp,vq ∈ G\Z(G), vp ≠ vq, are adjacent whenever vpvq = vq vp . In recent years, there has been significant research into the energy of graphs, particularly focusing on matrices associated with the degree of vertices. Therefore, motivated by that, our study elaborates on the energy of ΓG for dihedral groups of order 2n, D2n, concerning some graph matrices related to the degree of elements of D2n\Z(D2n) and examine the correlation between those energies. The matrices involved are known as geometric-arithmetic, symmetric division deg, degree exponent, inverse sum indeg and Sombor matrices. Based on these five matrices, it is found that the lowest graph energy is the geometric-arithmetic energy of ΓG whilst the highest is the degree exponent energy. Furthermore, the geometric-arithmetic, symmetric division deg, and degree exponent energies are always positive even integers. In contrast, the inverse sum indeg energy is a positive integer that can be either even or odd. Meanwhile, the Sombor energy is never an odd integer. Lviv Polytechnic National University 2025 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/121047/1/121047.pdf Romdhini, Mamika Ujianita and Nawawi, Athirah (2025) Degree-based energies of commuting graph for dihedral groups. Mathematical Modeling and Computing, 12 (3). pp. 832-840. ISSN 2312-9794; eISSN: 2415-3788 https://science.lpnu.ua/mmc/all-volumes-and-issues/volume-12-number-3-2025/degree-based-energies-commuting-graph-dihedral 10.23939/mmc2025.03.832 |
| spellingShingle | Romdhini, Mamika Ujianita Nawawi, Athirah Degree-based energies of commuting graph for dihedral groups |
| title | Degree-based energies of commuting graph for dihedral groups |
| title_full | Degree-based energies of commuting graph for dihedral groups |
| title_fullStr | Degree-based energies of commuting graph for dihedral groups |
| title_full_unstemmed | Degree-based energies of commuting graph for dihedral groups |
| title_short | Degree-based energies of commuting graph for dihedral groups |
| title_sort | degree-based energies of commuting graph for dihedral groups |
| url | http://psasir.upm.edu.my/id/eprint/121047/ http://psasir.upm.edu.my/id/eprint/121047/ http://psasir.upm.edu.my/id/eprint/121047/ http://psasir.upm.edu.my/id/eprint/121047/1/121047.pdf |