On a Graph Associated to UP-Algebras

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 gra...

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Bibliographic Details
Published inMathematical and computational applications Vol. 23; no. 4; p. 61
Main Authors Ansari, Moin A., Haidar, Azeem, Koam, Ali N.A.
Format Journal Article
LanguageEnglish
Published MDPI AG 01.12.2018
Subjects
annihilator ideal
graph folding
graph of equivalence classes
UP-algebra
UP-ideal
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Summary: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.
ISSN:2297-8747
2297-8747
DOI:10.3390/mca23040061