Sains Malaysiana 52(7)(2023): 2127-2137
http://doi.org/10.17576/jsm-2023-5207-18
Signless Laplacian Energy of Interval-Valued Fuzzy Graph and Its Applications
(Tenaga Laplacian Tanpa Tanda bagi Graf Kabur Bernilai-Selang dan Aplikasinya)
MAMIKA UJIANITA ROMDHINI1,*, FAISAL AL-SHARQI2, ATHIRAH NAWAWI3, ASHRAF AL-QURAN4& HOSSEIN RASHMANLOU5
1Department of Mathematics, Faculty of Mathematics
and Natural Science, Universitas Mataram, Mataram 83125, Indonesia
2Department of Mathematics, College of Education for Pure Sciences,
University of Anbar, Iraq
3Department of Mathematics and Statistics, Faculty of Science, Universiti Putra
Malaysia, 43400 Serdang, Selangor, Malaysia
4Basic Sciences Department,
Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia
5School of Physics, Damghan University, Damghan, Iran
Diserahkan: 22 Februari 2023/Diterima: 21 Jun 2023
Abstract
An interval-valued fuzzy graph (IVFG) emanates from a fuzzy graph (FG)
where the membership is given in interval form. This framework give the
user more flexibility in dealing with fuzzy information. In this paper, the
signless Laplacian matrix of an interval-valued fuzzy-directed graph is defined. The eigenvalue,
spectrum, spectral radius, and energy of an interval-valued fuzzy-directed
graph associated with the signless Laplacian matrix are reported. In addition,
the lower bound of the signless Laplacian energy in this graph is highlighted.
Finally, these tools are
employed to build an algorithm that helps in solving some real live problems.
Keywords: Energy of a graph; interval-valued fuzzy graph; signless Laplacian matrix
Abstrak
Graf kabur bernilai-selang (GKBS) terpancar daripada graf
kabur (GK) dengan keahliannya diberi dalam bentuk selang. Rangka kerja ini memberikan
pengguna lebih keluwesan dalam menangani maklumat
kabur. Dalam makalah ini, matriks Laplacian tanpa tanda bagi graf berarah kabur bernilai-selang ditakrifkan. Nilai eigen, spektrum,
jejari spektrum dan tenaga bagi graf berarah kabur bernilai-selang yang dikaitkan
dengan matriks Laplacian tanpa tanda dilaporkan. Di samping itu, sempadan bawah tenaga tanpa tanda Laplacian dalam graf ini diserlahkan. Akhir sekali, alat ini digunakan untuk
membina algoritma yang membantu menyelesaikan beberapa masalah dalam kehidupan
sebenar.
Kata
kunci: Graf kabur bernilai-selang; matriks Laplacian tanpa tanda; tenaga graf
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*Pengarang untuk surat-menyurat; email:
mamika@unram.ac.id
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