On connected cayley graphs of semigroups
© 2015 by the Mathematical Association of Thailand. All rights reserved. It is well known that for a finite group G with a nonempty subset A, the Cayley graph of G with respect to A is connected if and only if A is a generating set of G. In this paper we generalize this result to the case of semigro...
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| Main Authors: | , |
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| 格式: | 雜誌 |
| 出版: |
2018
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| 在線閱讀: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84952908237&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/44021 |
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| 總結: | © 2015 by the Mathematical Association of Thailand. All rights reserved. It is well known that for a finite group G with a nonempty subset A, the Cayley graph of G with respect to A is connected if and only if A is a generating set of G. In this paper we generalize this result to the case of semigroups and give some necessary and sufficient conditions for Cayley graphs of a semigroup to be connected. We also characterize weakly connected Cayley graphs of a semigroup and indicate a relationship between a Cayley graph of a semigroup and the Hasse diagram of a partially ordered set. |
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