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 ROMDHINI^1,*, 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

Received: 22 February 2023/Accepted: 21 June 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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*Corresponding author; email: mamika@unram.ac.id