OPTICAL ART OF A PLANAR IDEMPOTENT DIVISOR GRAPH OF COMMUTATIVE RING
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Published:2024-03-30
Issue:1
Volume:24
Page:123-132
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ISSN:2068-3049
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Container-title:Journal of Science and Arts
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language:en
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Short-container-title:J. Sci. Arts
Author:
AUTHMAN MOHAMMED N.1, MOHAMMAD HUSAM Q.2, SHUKER NAZAR H.2
Affiliation:
1. Iraqi Ministry of Education, Open Educational College, Department of Mathematics, Mosul, Iraq. 2. University of Mosul, College of Computer Science and Mathematics, Department of Mathematics, Mosul, Iraq.
Abstract
The idempotent divisor graph of a commutative ring R is a graph with a vertex set in R* = R-{0}, where any distinct vertices x and y are adjacent if and only if x.y = e, for some non-unit idempotent element e^2 = e ∈ R, and is denoted by Л(R). Our goal in this work is to transform the planar idempotent divisor graph after coloring its regions into optical art by depending on the reflection of vertices, edges, and planes on the x or y-axes. That is, we achieve Op art solely through pure mathematics in this paper.
Publisher
Valahia University of Targoviste - Journal of Science and Arts
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