THE TRIPLE IDENTITY GRAPH OF THE RING Z_n

  • Vika Yugi Kurniawan Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia https://orcid.org/0000-0001-8475-7243
  • Chessa Fanny Ekasiwi Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia https://orcid.org/0009-0008-3328-7817
  • Santoso Budi Wiyono Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia https://orcid.org/0000-0002-2377-1890
DOI: https://doi.org/10.30598/barekengvol19iss4pp2521-2530
Keywords: Algebraic Graph, Diameter, Girth, Hamiltonian Graph, Identity Element

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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Published
2025-09-01
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.
Issue
Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

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

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