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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Ekasiwi, Chessa Fanny
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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ALGORITHM FOR CONSTRUCTING TRIPLE IDENTITY GRAPH OF RING Z_n USING PYTHON Kurniawan, Vika Yugi; Ekasiwi, Chessa Fanny
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss3pp1629-1638

Abstract

Let R be a commutative ring. The triple identity graph of ring R is denoted by TE(R) with sets of vertices Two different vertices and are adjacent if and only if there is an element in such that and . To easily visualize the triple identity graph, a program is needed to represent it briefly. Python can easily manipulate, analyze, and visualize data. Therefore, this study uses Python to construct the algorithm for In this research, some examples will be given and then be observed for new characteristics of the triple identity graph of ring such as the connectedness, the diameter, and the girth. And we find the characterize for which graph is empty, connected, or Hamiltonian.
THE TRIPLE IDENTITY GRAPH OF THE RING Z_n Kurniawan, Vika Yugi; Ekasiwi, Chessa Fanny; Wiyono, Santoso Budi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2521-2530

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 .
Co-Authors Santoso Budi Wiyono Vika Yugi Kurniawan