International Journal of Fuzzy Mathematical Archive
  • Year: 2024
  • Volume: 22
  • Issue: 1

On spectrum and energy of fuzzy graphs

  • Author:
  • Mamika Ujianita Romdhini1, Hossein Rashmanlou2, Faisal Al-Sharqi3, I Wayan Sudiarta4, Ahmed Abbas Jasim Al-Hchaimi5
  • Total Page Count: 11
  • Page Number: 33 to 43

1Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram, Mataram, 83125, Indonesia, E-mail: mamika@unram.ac.id

2School of Physics, Damghan University, Damghan, Iran, E-mail: rashmanlou.1987@gmail.com

3Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq, E-mail: faisal.ghazi@uoanbar.edu.iq

4Department of Physics, Faculty of Mathematics and Natural Sciences, University of Mataram, Mataram, 83125, Indonesia, E-mail: wayan.sudiarta@unram.ac.id

5Department of Electromechanical Systems Engineering, Thiqar Technical College, Southern Technical University, Basra, Iraq, E-mail: ahmed.alhchaimi@stu.edu.iq

Online published on 25 June, 2025.

Abstract

The idea of fuzzy graphs was proposed by Rosenfeld as a generalization of Euler's graph theory. The relationship between a fuzzy graph and its adjacency matrix presents the spectrum formula of a fuzzy graph. The concept of energy is closely related to the spectrum of a graph This study focuses on the weighted fuzzy graph. We provide the eigenvalue, spectrum, spectral radius, and energy of a fuzzy graph associated with the adjacency matrix. Ultimately, we utilize these tools to construct an algorithm that effectively addresses energy determination from fuzzy graphs.

Keywords

Fuzzy graph, Energy of a graph, Adjacency matrix