On the semigroup whose elements are subgraphs of a complete graph
© 2018 by the author. Let Knbe a complete graph on n vertices. Denote by SKnthe set of all subgraphs of Kn. For each G, H ∈ SKn, the ring sum of G and H is a graph whose vertex set is V(G) ∪ V(H) and whose edges are that of either G or H, but not of both. Then SKnis a semigroup under the ring sum. I...
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th-cmuir.6653943832-588052018-09-05T04:32:42Z On the semigroup whose elements are subgraphs of a complete graph Yanisa Chaiya Chollawat Pookpienlert Nuttawoot Nupo Sayan Panma Mathematics © 2018 by the author. Let Knbe a complete graph on n vertices. Denote by SKnthe set of all subgraphs of Kn. For each G, H ∈ SKn, the ring sum of G and H is a graph whose vertex set is V(G) ∪ V(H) and whose edges are that of either G or H, but not of both. Then SKnis a semigroup under the ring sum. In this paper, we study Green's relations on SKnand characterize ideals, minimal ideals, maximal ideals, and principal ideals of SKn. Moreover, maximal subsemigroups and a class of maximal congruences are investigated. Furthermore, we prescribe the natural order on SKnand consider minimal elements, maximal elements and covering elements of SKnunder this order. 2018-09-05T04:32:42Z 2018-09-05T04:32:42Z 2018-05-09 Journal 22277390 2-s2.0-85046620077 10.3390/math6050076 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85046620077&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58805 |
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Mathematics |
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Mathematics Yanisa Chaiya Chollawat Pookpienlert Nuttawoot Nupo Sayan Panma On the semigroup whose elements are subgraphs of a complete graph |
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© 2018 by the author. Let Knbe a complete graph on n vertices. Denote by SKnthe set of all subgraphs of Kn. For each G, H ∈ SKn, the ring sum of G and H is a graph whose vertex set is V(G) ∪ V(H) and whose edges are that of either G or H, but not of both. Then SKnis a semigroup under the ring sum. In this paper, we study Green's relations on SKnand characterize ideals, minimal ideals, maximal ideals, and principal ideals of SKn. Moreover, maximal subsemigroups and a class of maximal congruences are investigated. Furthermore, we prescribe the natural order on SKnand consider minimal elements, maximal elements and covering elements of SKnunder this order. |
| format |
Journal |
| author |
Yanisa Chaiya Chollawat Pookpienlert Nuttawoot Nupo Sayan Panma |
| author_facet |
Yanisa Chaiya Chollawat Pookpienlert Nuttawoot Nupo Sayan Panma |
| author_sort |
Yanisa Chaiya |
| title |
On the semigroup whose elements are subgraphs of a complete graph |
| title_short |
On the semigroup whose elements are subgraphs of a complete graph |
| title_full |
On the semigroup whose elements are subgraphs of a complete graph |
| title_fullStr |
On the semigroup whose elements are subgraphs of a complete graph |
| title_full_unstemmed |
On the semigroup whose elements are subgraphs of a complete graph |
| title_sort |
on the semigroup whose elements are subgraphs of a complete graph |
| publishDate |
2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85046620077&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58805 |
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