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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| Format: | Article |
| Language: | English |
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MDPI AG
2018-10-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | http://www.mdpi.com/2297-8747/23/4/61 |
| _version_ | 1818291260592488448 |
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| author | Moin A. Ansari Azeem Haidar Ali N.A. Koam |
| author_facet | Moin A. Ansari Azeem Haidar Ali N.A. Koam |
| author_sort | Moin A. Ansari |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T02:41:14Z |
| format | Article |
| id | doaj.art-fe220c4290504805b960850ef3f5dea2 |
| institution | Directory Open Access Journal |
| issn | 2297-8747 |
| language | English |
| last_indexed | 2024-12-13T02:41:14Z |
| publishDate | 2018-10-01 |
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| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-fe220c4290504805b960850ef3f5dea22022-12-22T00:02:17ZengMDPI AGMathematical and Computational Applications2297-87472018-10-012346110.3390/mca23040061mca23040061On a Graph Associated to UP-AlgebrasMoin A. Ansari0Azeem Haidar1Ali N.A. Koam2Department of Mathematics, College of Science, Jazan University, New Campus, P.O. Box 2097, Jazan, Saudi ArabiaDepartment of Mathematics, College of Science, Jazan University, New Campus, P.O. Box 2097, Jazan, Saudi ArabiaDepartment of Mathematics, College of Science, Jazan University, New Campus, P.O. Box 2097, Jazan, Saudi ArabiaIn 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.http://www.mdpi.com/2297-8747/23/4/61UP-algebraUP-idealannihilator idealgraph of equivalence classesgraph folding |
| spellingShingle | Moin A. Ansari Azeem Haidar Ali N.A. Koam On a Graph Associated to UP-Algebras Mathematical and Computational Applications UP-algebra UP-ideal annihilator ideal graph of equivalence classes graph folding |
| title | On a Graph Associated to UP-Algebras |
| title_full | On a Graph Associated to UP-Algebras |
| title_fullStr | On a Graph Associated to UP-Algebras |
| title_full_unstemmed | On a Graph Associated to UP-Algebras |
| title_short | On a Graph Associated to UP-Algebras |
| title_sort | on a graph associated to up algebras |
| topic | UP-algebra UP-ideal annihilator ideal graph of equivalence classes graph folding |
| url | http://www.mdpi.com/2297-8747/23/4/61 |
| work_keys_str_mv | AT moinaansari onagraphassociatedtoupalgebras AT azeemhaidar onagraphassociatedtoupalgebras AT alinakoam onagraphassociatedtoupalgebras |