on the semigroup whose elements are subgraphs of a complete graph
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ID: 161519
2018
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Abstract
Let K n be a complete graph on n vertices. Denote by S K n the set of all subgraphs of K n . For each G , H ∈ S K n , 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 S K n is a semigroup under the ring sum. In this paper, we study Green’s relations on S K n and characterize ideals, minimal ideals, maximal ideals, and principal ideals of S K n . Moreover, maximal subsemigroups and a class of maximal congruences are investigated. Furthermore, we prescribe the natural order on S K n and consider minimal elements, maximal elements and covering elements of S K n under this order.
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chaiya2018mathematicson
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| Authors | ;Yanisa Chaiya;Chollawat Pookpienlert;Nuttawoot Nupo;Sayan Panma |
| Journal | Turkish journal of pharmaceutical sciences |
| Year | 2018 |
| DOI |
10.3390/math6050076
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