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Degree subtraction energy of commuting and non-commuting graphs for dihedral groups

Let ¯ ΓG and ΓG be the commuting and non-commuting graphs on a finite group G, respectively, having G\Z(G) as the vertex set, where Z(G) is the center of G. The order of ¯ ΓG and ΓG is |G\Z(G)|, denoted by m. For ΓG, the edge joining two distinct vertices vp,vq ∈ G\Z(G) if and only if vpvq= vqvp, on...

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Main Authors: Romdhini, Mamika Ujianita, Nawawi, Athirah
Format: Article
Language:English
Published: Badih Ghusayni 2023
Online Access:http://psasir.upm.edu.my/id/eprint/107222/1/Degree%20subtraction%20energy%20of%20commuting%20and%20non-commuting%20graphs%20for%20dihedral%20groups.pdf
http://psasir.upm.edu.my/id/eprint/107222/
https://future-in-tech.net/18.3/R-MathTech22-Romdhini-Nawawi.pdf
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spelling my.upm.eprints.1072222024-10-17T03:41:43Z http://psasir.upm.edu.my/id/eprint/107222/ Degree subtraction energy of commuting and non-commuting graphs for dihedral groups Romdhini, Mamika Ujianita Nawawi, Athirah Let ¯ ΓG and ΓG be the commuting and non-commuting graphs on a finite group G, respectively, having G\Z(G) as the vertex set, where Z(G) is the center of G. The order of ¯ ΓG and ΓG is |G\Z(G)|, denoted by m. For ΓG, the edge joining two distinct vertices vp,vq ∈ G\Z(G) if and only if vpvq= vqvp, on the other hand, whenever they commute in G, vp and vq are adjacent in ¯ ΓG. The degree subtraction matrix (DSt) of ΓG is denoted by DSt(ΓG), so that its (p,q)−entry is equal to dvp − dvq , if vp= vq, and zero if vp = vq, where dvp is the degree of vp. For i =1,2,...,m, the maximum of |λi| as the DSt−spectral radius of ΓG and the sum of |λi| as DSt−energy of ΓG, where λi are the eigenvalues of DSt(ΓG). These notations can be applied analogously to the degree subtraction matrix of the commuting graph, DSt(¯ ΓG). Throughout this paper, we provide DSt−spectral radius and DSt−energy of ΓG and ¯ ΓG for dihedral groups of order 2n, where n ≥ 3. We then present the correlation of the energies and their spectral radius. Badih Ghusayni 2023-03-31 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/107222/1/Degree%20subtraction%20energy%20of%20commuting%20and%20non-commuting%20graphs%20for%20dihedral%20groups.pdf Romdhini, Mamika Ujianita and Nawawi, Athirah (2023) Degree subtraction energy of commuting and non-commuting graphs for dihedral groups. International Journal of Mathematics and Computer Science, 18 (3). 497 - 508. ISSN 1814-0432 https://future-in-tech.net/18.3/R-MathTech22-Romdhini-Nawawi.pdf
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description Let ¯ ΓG and ΓG be the commuting and non-commuting graphs on a finite group G, respectively, having G\Z(G) as the vertex set, where Z(G) is the center of G. The order of ¯ ΓG and ΓG is |G\Z(G)|, denoted by m. For ΓG, the edge joining two distinct vertices vp,vq ∈ G\Z(G) if and only if vpvq= vqvp, on the other hand, whenever they commute in G, vp and vq are adjacent in ¯ ΓG. The degree subtraction matrix (DSt) of ΓG is denoted by DSt(ΓG), so that its (p,q)−entry is equal to dvp − dvq , if vp= vq, and zero if vp = vq, where dvp is the degree of vp. For i =1,2,...,m, the maximum of |λi| as the DSt−spectral radius of ΓG and the sum of |λi| as DSt−energy of ΓG, where λi are the eigenvalues of DSt(ΓG). These notations can be applied analogously to the degree subtraction matrix of the commuting graph, DSt(¯ ΓG). Throughout this paper, we provide DSt−spectral radius and DSt−energy of ΓG and ¯ ΓG for dihedral groups of order 2n, where n ≥ 3. We then present the correlation of the energies and their spectral radius.
format Article
author Romdhini, Mamika Ujianita
Nawawi, Athirah
spellingShingle Romdhini, Mamika Ujianita
Nawawi, Athirah
Degree subtraction energy of commuting and non-commuting graphs for dihedral groups
author_facet Romdhini, Mamika Ujianita
Nawawi, Athirah
author_sort Romdhini, Mamika Ujianita
title Degree subtraction energy of commuting and non-commuting graphs for dihedral groups
title_short Degree subtraction energy of commuting and non-commuting graphs for dihedral groups
title_full Degree subtraction energy of commuting and non-commuting graphs for dihedral groups
title_fullStr Degree subtraction energy of commuting and non-commuting graphs for dihedral groups
title_full_unstemmed Degree subtraction energy of commuting and non-commuting graphs for dihedral groups
title_sort degree subtraction energy of commuting and non-commuting graphs for dihedral groups
publisher Badih Ghusayni
publishDate 2023
url http://psasir.upm.edu.my/id/eprint/107222/1/Degree%20subtraction%20energy%20of%20commuting%20and%20non-commuting%20graphs%20for%20dihedral%20groups.pdf
http://psasir.upm.edu.my/id/eprint/107222/
https://future-in-tech.net/18.3/R-MathTech22-Romdhini-Nawawi.pdf
_version_ 1814054625563639808
score 13.211869

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