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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| Main Authors: | , , , |
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| Format: | Journal |
| Published: |
2018
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| Subjects: | |
| Online Access: | 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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| Institution: | Chiang Mai University |
| Summary: | © 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. |
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