Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Articles

ENERGY OF NON-COPRIME GRAPH ON MODULO GROUP

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  • Gusti Yogananda Karang,
  • I Gede Adhitya Wisnu Wardhana,
  • Manimaran Angamuthu
Gusti Yogananda Karang
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Mataram, Indonesia
I Gede Adhitya Wisnu Wardhana
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Mataram, Indonesia
Manimaran Angamuthu
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, India
DOI: https://doi.org/10.30598/barekengvol19iss4pp2937-2952
Published September 1, 2025
Keywords
  • C Non-Coprime Graph,
  • Graph Energy,
  • Graph Theory,
  • Modulo Group
How to Cite
[1]
G. Y. Karang, I. G. A. Wisnu Wardhana, and M. Angamuthu, “ENERGY OF NON-COPRIME GRAPH ON MODULO GROUP”, BAREKENG: J. Math. & App., vol. 19, no. 4, pp. 2937-2952, Sep. 2025.

Copyright (c) 2025 I Gede Adhitya Wisnu Wardhana, Gusti Yogananda Karang, Manimaran Angamuthu

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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

A graph is a mathematical structure consisting of a non-empty set of vertices and a set of edges connecting these vertices. In recent years, extensive research on graphs has been conducted, with one of the intriguing topics being the representation of graphs within algebraic structures, particularly groups. This approach bridges two areas of mathematics: graph theory and algebra. This study focuses on graph representation, specifically non-coprime graphs in the group of integers modulo ​, where ,  is a prime number, and  is a non-negative integer. The non-coprime graph of a group  is defined as a graph with the vertex set , where  is the identity element of . Two distinct vertices  and  are connected by an edge if . Specifically, this research investigates the Sombor energy, the Degree Sum energy, the Degree Exponent Sum energy, the Laplacian energy, the Distance Laplacian energy, and the Distance Signless Laplacian energy of a non-coprime graph on a modulo group.

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