Sains Malaysiana 53(6)(2024): 1421-1426

http://doi.org/10.17576/jsm-2024-5306-15

 

Degree Square Subtraction Energy of Non-Commuting Graph for Dihedral Groups 

(Tenaga Tolak Darjah Kuasa Dua bagi Graf Tak Kalis Tukar Tertib untuk Kumpulan Dwihedron)

 

MAMIKA UJIANITA ROMDHINI1,*, ATHIRAH NAWAWI2, FAISAL AL-SHARQI3,4,* & MUHAMMAD RIJAL ALFIAN1                 

1Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Mataram, Mataram 83125, Indonesia 

2Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

3Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq

4College of Engineering, National University of Science and Technology, Dhi Qar, Iraq

 

Diserahkan: 10 Oktober 2023/Diterima: 26 April 2024


Abstract

The non-commuting graph on a finite , denoted by , with the set of non-central elements of as the vertex set and two distinct vertices are adjacent whenever they do not commute in . In this paper, we discuss the spectrum, spectral radius and degree square subtraction energy of  for dihedral groups of order ,  where . It is found that the obtained energy here is equal to twice its spectral radius and there is a relationship with the degree subtraction energy that was described in previous literature.

 

Keywords: Degree square subtraction matrix; dihedral group; non-commuting graph; the energy of a graph         

Abstrak

Graf tak kalis tukar tertib ditakrifkan pada suatu kumpulan terhingga , ditandakan dengan , dengan set unsur bukan pusat  sebagai set bucu dan dua bucu berbeza adalah bersebelahan apabila mereka tak kalis tukar tertib dalam . Dalam makalah ini, kita membincangkan spektrum, jejari spektrum dan tenaga tolak darjah kuasa dua bagi  untuk kumpulan dwihedron peringkat , , yang . Didapati bahawa tenaga yang diperoleh ini adalah sama dengan dua kali jejari spektrumnya dan terdapat hubungan dengan tenaga tolak darjah yang telah diterangkan dalam kajian terdahulu.

 

Kata kunci: Graf tak kalis tukar tertib; kumpulan dwihedron; matriks tolak darjah kuasa dua; tenaga graf

 

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*Pengarang untuk surat-menyurat; email: mamika@unram.ac.id

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

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