Graphs Based on Hoop Algebras

Mona Aaly Kologani, Rajab Ali Borzooei and Hee Sik Kim
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Mona Aaly Kologani: Hatef Higher Education Institute, Zahedan 8301, Iran
Rajab Ali Borzooei: Department of Mathematics, Shahid Beheshti University, Tehran 7561, Iran
Hee Sik Kim: Research Institute for Natural Science, Department of Mathematics, Hanyang University, Seoul 04763, Korea

Mathematics, 2019, vol. 7, issue 4, 1-14

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.

Keywords: hoop algebra; zero divisor; implicative graph; productive graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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