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When is the Cayley graph of a semigroup isomorphic to the Cayley graph of a group

In: Mathematica Slovaca, vol. 67, no. 1
Shoufeng Wang
Detaily:
Rok, strany: 2017, 33 - 40
Kľúčové slová:
Cayley graphs of semigroups, vertex-transitive graphs, Cayley graphs of groups
O článku:
It is well known that Cayley graphs of groups are automatically vertex-transitive. A pioneer result of Kelarev and Praeger implies that Cayley graphs of semigroups can be regarded as a source of possibly new vertex-transitive graphs. In this note, we consider the following problem: Is every vertex-transitive Cayley graph of a semigroup isomorphic to a Cayley graph of a group? With the help of the results of Kelarev and Praeger, we show that the vertex-transitive, connected and undirected finite Cayley graphs of semigroups are isomorphic to Cayley graphs of groups, and all finite vertex-transitive Cayley graphs of inverse semigroups are isomorphic to Cayley graphs of groups. Furthermore, some related problems are proposed.
Ako citovať:
ISO 690:
Wang, S. 2017. When is the Cayley graph of a semigroup isomorphic to the Cayley graph of a group. In Mathematica Slovaca, vol. 67, no.1, pp. 33-40. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0245

APA:
Wang, S. (2017). When is the Cayley graph of a semigroup isomorphic to the Cayley graph of a group. Mathematica Slovaca, 67(1), 33-40. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0245
O vydaní:
Publikované: 1. 2. 2017