Graphs Based on Hoop Algebras

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 prod...

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Bibliographic Details
Published in:Mathematics (Basel) 2019-04, Vol.7 (4), p.362
Main Authors: Kologani, Mona Aaly, Borzooei, Rajab Ali, Kim, Hee Sik
Format: Article
Language:English
Subjects:
Computer science
Graphs
hoop algebra
implicative graph
Investigations
Mathematics
productive graph
zero divisor
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7040362