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On a Graph Associated to UP-Algebras

Department of Mathematics, College of Science, Jazan University, New Campus, P.O. Box 2097, Jazan, Saudi Arabia
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Math. Comput. Appl. 2018, 23(4), 61; https://doi.org/10.3390/mca23040061
Received: 20 September 2018 / Revised: 11 October 2018 / Accepted: 12 October 2018 / Published: 15 October 2018
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Abstract

In this article, we introduce the concept of graphs associated with commutative UP-algebra, which we say is a UP-graph whose vertices are the elements of commutative UP-algebra and whose edges are the association of two vertices, that is two elements from commutative UP-algebra. We also define a graph of equivalence classes of a commutative UP-algebra and prove some related results based on the algebraic properties of the graph. We show that two graphs are the same and complete bipartite if they are formed by equivalence classes of UP-algebra and the graph folding of commutative UP-algebra. An algorithm for checking whether a given set is a UP-algebra or not has also been given. View Full-Text
Keywords: UP-algebra; UP-ideal; annihilator ideal; graph of equivalence classes; graph folding UP-algebra; UP-ideal; annihilator ideal; graph of equivalence classes; graph folding
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Ansari, M.A.; Haidar, A.; Koam, A.N. On a Graph Associated to UP-Algebras. Math. Comput. Appl. 2018, 23, 61.

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