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Graphs Based on Hoop Algebras

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mona Aaly Kologani & Rajab Ali Borzooei & Hee Sik Kim, 2019. "Graphs Based on Hoop Algebras," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:362-:d:224737
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    References listed on IDEAS

    as
    1. Young Bae Jun & Kyoung Ja Lee, 2011. "Graphs Based on BCK/BCI-Algebras," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-8, January.
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