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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