THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n

  • Vika Yugi Kurniawan Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Sebelas Maret, Indonesia https://orcid.org/0000-0001-8475-7243
  • Bayu Purboutomo Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Sebelas Maret, Indonesia https://orcid.org/0009-0008-6472-0054
  • Nughthoh Arfawi Kurdhi Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Sebelas Maret, Indonesia https://orcid.org/0000-0001-9274-1807
DOI: https://doi.org/10.30598/barekengvol19iss3pp2219-2228
Keywords: Diameter, Eulerian, Girth, Hamiltonian, Ring Z_n, The Triple Idempotent Graph

Abstract

Let  be a commutative ring, and  denote the set of all idempotent elements of . The triple idempotent graph of , denoted by , is defined as an undirected simple graph whose vertex set . Two distinct vertices u and v in  are adjacent if and only if there exists  where  and  such that , and . This definition generalizes the notion of an idempotent divisor graph by involving a triple product, which allows deeper exploration of the combinatorial behavior of idempotents in rings. In this research, we investigate the properties of the triple idempotent graph of the ring of integers modulo n, denoted by . As a results, we establish that  and , provided that the graph is connected. Furthermore,  is Hamiltonian if n is a prime and , and Eulerian if n is a prime and .

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Published
2025-07-01
How to Cite
[1]
V. Y. Kurniawan, B. Purboutomo, and N. A. Kurdhi, “THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n”, BAREKENG: J. Math. & App., vol. 19, no. 3, pp. 2219-2228, Jul. 2025.
Issue
Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2025 Vika Yugi Kurniawan, Bayu Purboutomo, Nughthoh Arfawi Kurdhi

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