The endomorphism monoids and automorphism groups of Cayley graphs of semigroups

2017 ◽  
Vol 95 (1) ◽  
pp. 179-191 ◽  
Author(s):  
Behnam Khosravi
Keyword(s):  
Automorphism Groups ◽  
Cayley Graphs ◽  
Endomorphism Monoids ◽  
Cayley Graphs Of Semigroups

Generalized Cayley graphs of semigroups I

2011 ◽  
Vol 84 (1) ◽  
pp. 131-143 ◽  
Author(s):  
Yongwen Zhu
Keyword(s):  
Cayley Graphs ◽  
Cayley Graphs Of Semigroups

scholarly journals Finite n-quandles of torus and two-bridge links

2019 ◽  
Vol 28 (03) ◽  
pp. 1950028
Author(s):  
Alissa S. Crans ◽  
Blake Mellor ◽  
Patrick D. Shanahan ◽  
Jim Hoste
Keyword(s):  
Automorphism Groups ◽  
Cayley Graphs ◽  
Torus Knots ◽  
Knots And Links ◽  
Torus Links

We compute Cayley graphs and automorphism groups for all finite [Formula: see text]-quandles of two-bridge and torus knots and links, as well as torus links with an axis.

Generalized Cayley graphs of semigroups II

2011 ◽  
Vol 84 (1) ◽  
pp. 144-156 ◽  
Author(s):  
Yongwen Zhu
Keyword(s):  
Cayley Graphs ◽  
Cayley Graphs Of Semigroups

scholarly journals A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A119

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2935
Author(s):  
Bo Ling ◽  
Wanting Li ◽  
Bengong Lou
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Automorphism Groups ◽  
Cayley Graphs ◽  
Vital Role ◽  
Alternating Group ◽  
Full Automorphism Group ◽  
Base Group

A Cayley graph Γ=Cay(G,S) is said to be normal if the base group G is normal in AutΓ. The concept of the normality of Cayley graphs was first proposed by M.Y. Xu in 1998 and it plays a vital role in determining the full automorphism groups of Cayley graphs. In this paper, we construct an example of a 2-arc transitive hexavalent nonnormal Cayley graph on the alternating group A119. Furthermore, we determine the full automorphism group of this graph and show that it is isomorphic to A120.

Frobenius REA-groups and their Cayley graphs

2019 ◽  
pp. 2150007
Author(s):  
Lei Wang ◽  
Shou Hong Qiao
Keyword(s):  
Cayley Graph ◽  
Automorphism Groups ◽  
Cayley Graphs ◽  
Frobenius Groups ◽  
Edge Transitive

In this paper, we determine the automorphism groups of a class of Frobenius groups, and then solve that under what condition they are REA-groups. As an application, we construct a type of normal edge-transitive Cayley graph.

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

2017 ◽  
Vol 67 (1) ◽  
Author(s):  
Shoufeng Wang
Keyword(s):  
Cayley Graph ◽  
Cayley Graphs ◽  
Inverse Semigroups ◽  
Graphs Of Groups ◽  
Cayley Graphs Of Semigroups ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs

AbstractIt 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.

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