Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups
The neighbors degree sum (NDS) energy of a graph is determined by the sum of its absolute eigenvalues from its corresponding neighbors degree sum matrix. The non-diagonal entries of NDS−matrix are the summation of the degree of two adjacent vertices, or it is zero for non-adjacent vertices, whereas...
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Universiti Putra Malaysia
2023
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my.upm.eprints.1085482024-10-11T07:47:17Z http://psasir.upm.edu.my/id/eprint/108548/ Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups Romdhini, M. U. Nawawi, A. Chen, C. Y. The neighbors degree sum (NDS) energy of a graph is determined by the sum of its absolute eigenvalues from its corresponding neighbors degree sum matrix. The non-diagonal entries of NDS−matrix are the summation of the degree of two adjacent vertices, or it is zero for non-adjacent vertices, whereas for the diagonal entries are the negative of the square of vertex degree. This study presents the formulas of neighbors degree sum energies of commuting and non-commuting graphs for dihedral groups of order 2n, D2n, for two cases−odd and even n. The results in this paper comply with the well known fact that energy of a graph is neither an odd integer nor a square root of an odd integer. Universiti Putra Malaysia 2023-03-27 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/108548/1/Neighbors%20Degree%20Sum%20Energy.pdf Romdhini, M. U. and Nawawi, A. and Chen, C. Y. (2023) Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups. Malaysian Journal of Mathematical Sciences, 17 (1). pp. 53-65. ISSN 1823-8343; ESSN: 2289-750X https://mjms.upm.edu.my/lihatmakalah.php?kod=2023/March/17/1/53-65 10.47836/mjms.17.1.05 |
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The neighbors degree sum (NDS) energy of a graph is determined by the sum of its absolute eigenvalues from its corresponding neighbors degree sum matrix. The non-diagonal entries of NDS−matrix are the summation of the degree of two adjacent vertices, or it is zero for non-adjacent vertices, whereas for the diagonal entries are the negative of the square of vertex degree. This study presents the formulas of neighbors degree sum energies of commuting and non-commuting graphs for dihedral groups of order 2n, D2n, for two cases−odd and even n. The results in this paper comply with the well known fact that energy of a graph is neither an odd integer nor a square root of an odd integer. |
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Article |
author |
Romdhini, M. U. Nawawi, A. Chen, C. Y. |
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Romdhini, M. U. Nawawi, A. Chen, C. Y. Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups |
author_facet |
Romdhini, M. U. Nawawi, A. Chen, C. Y. |
author_sort |
Romdhini, M. U. |
title |
Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups |
title_short |
Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups |
title_full |
Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups |
title_fullStr |
Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups |
title_full_unstemmed |
Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups |
title_sort |
neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups |
publisher |
Universiti Putra Malaysia |
publishDate |
2023 |
url |
http://psasir.upm.edu.my/id/eprint/108548/1/Neighbors%20Degree%20Sum%20Energy.pdf http://psasir.upm.edu.my/id/eprint/108548/ https://mjms.upm.edu.my/lihatmakalah.php?kod=2023/March/17/1/53-65 |
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