Graphs Based on Equality Algebras

M. Aaly Kologani (), G. Muhiuddin, R. A. Borzooei () and G. R. Rezaei ()
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M. Aaly Kologani: Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
G. Muhiuddin: ��Department of Mathematics, University of Tabuk, Tabuk, 71491, Saudi Arabia
R. A. Borzooei: Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
G. R. Rezaei: Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

New Mathematics and Natural Computation (NMNC), 2023, vol. 19, issue 01, 67-85

Abstract: In this paper, we introduce new kinds of graphs based on equality algebras. First of all, by using the meet operation we define the notion of zero divisors on equality algebra and study related properties. Then we introduce a meet graph on equality algebra by using zero divisors. In addition, we investigate some conditions for a meet graph to be a complete, connected and a star graph. Also, by using the notion of filters in equality algebras, we define an equivalence relation on equality algebras and then by using the equivalence classes we introduce two kinds of graphs on them. Finally, conditions for a graph based on these classes to be connected, or bipartite, or complete, or planar or an outer-planar graph are provided.

Keywords: Equality algebra; graph; zero divisor; filter; planar graph; outer-planar graph (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S1793005722500491

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