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

THE TRIPLE IDENTITY GRAPH OF THE RING Z_n

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  • Vika Yugi Kurniawan,
  • Chessa Fanny Ekasiwi,
  • Santoso Budi Wiyono
Vika Yugi Kurniawan
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia
Chessa Fanny Ekasiwi
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia
Santoso Budi Wiyono
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia
DOI: https://doi.org/10.30598/barekengvol19iss4pp2521-2530
Published September 1, 2025
Keywords
  • Algebraic Graph,
  • Diameter,
  • Girth,
  • Hamiltonian Graph,
  • Identity Element
How to Cite
[1]
V. Y. Kurniawan, C. F. Ekasiwi, and S. B. Wiyono, “THE TRIPLE IDENTITY GRAPH OF THE RING Z_n”, BAREKENG: J. Math. & App., vol. 19, no. 4, pp. 2521-2530, Sep. 2025.

Copyright (c) 2025 Vika Yugi Kurniawan, Chessa Fanny Ekasiwi; Santoso Budi Wiyono

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

Abstract

Let  be a commutative ring with identity and  is an identity element of . The triple identity graph of the ring , represented by ), is an undirected simple graph with the vertex set . In , two different vertices  and  is called adjacent if there is an element such that and . The triple identity graph of the ring of integers modulo , represented by , is the subject of this study. We obtain several results regarding the properties of the graph , which are summarized as follows. The graph  is a connected graph if and only if  is prime and . If  is connected, then diam and gr. Furthermore,  is a Hamiltonian graph if  is a prime number and .

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