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Graphs Based on Hoop Algebras

1
Hatef Higher Education Institute, Zahedan 8301, Iran
2
Department of Mathematics, Shahid Beheshti University, Tehran 7561, Iran
3
Research Institute for Natural Science, Department of Mathematics, Hanyang University, Seoul 04763, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(4), 362; https://doi.org/10.3390/math7040362
Received: 14 March 2019 / Revised: 13 April 2019 / Accepted: 17 April 2019 / Published: 21 April 2019
(This article belongs to the Special Issue General Algebraic Structures)
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Abstract

In this paper, we investigate the graph structures on hoop algebras. First, by using the quasi-filters and r-prime (one-prime) filters, we construct an implicative graph and show that it is connected and under which conditions it is a star or tree. By using zero divisor elements, we construct a productive graph and prove that it is connected and both complete and a tree under some conditions. View Full-Text
Keywords: hoop algebra; zero divisor; implicative graph; productive graph hoop algebra; zero divisor; implicative graph; productive graph
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Kologani, M.A.; Borzooei, R.A.; Kim, H.S. Graphs Based on Hoop Algebras. Mathematics 2019, 7, 362.

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