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Graphs Based on Hoop Algebras

Hatef Higher Education Institute, Zahedan 8301, Iran
Department of Mathematics, Shahid Beheshti University, Tehran 7561, Iran
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;
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)
PDF [274 KB, uploaded 25 April 2019]


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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