scholarly journals Automorphism groups of Cayley graphs generated by block transpositions and regular Cayley maps

2017 ◽  
Vol 340 (1) ◽  
pp. 3125-3139 ◽  
Author(s):  
Annachiara Korchmaros ◽  
István Kovács
Keyword(s):  
Automorphism Groups ◽  
Cayley Graphs ◽  
Cayley Maps

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.

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.

scholarly journals Automorphisms of Cayley graphs of metacyclic groups of prime-power order

2001 ◽  
Vol 71 (2) ◽  
pp. 223-232 ◽  
Author(s):  
Caiheng Li ◽  
Hyo-Seob Sim
Keyword(s):  
Graph Theory ◽  
Cayley Graph ◽  
Prime Power ◽  
Automorphism Groups ◽  
Cayley Graphs ◽  
Prime Power Order ◽  
Subsequent Work ◽  
Metacyclic Groups

AbstractThis paper inverstigates the automorphism groups of Cayley graphs of metracyclicp-gorups. A characterization is given of the automorphism groups of Cayley grahs of a metacyclicp-group for odd primep. In particular, a complete determiniation of the automophism group of a connected Cayley graph with valency less than 2pof a nonabelian metacyclicp-group is obtained as a consequence. In subsequent work, the result of this paper has been applied to solve several problems in graph theory.

scholarly journals Regular maps from Cayley graphs II antibalanced Cayley maps

1994 ◽  
Vol 124 (1-3) ◽  
pp. 179-191 ◽  
Author(s):  
Jozef Širáň ◽  
Martin Škoviera
Keyword(s):  
Cayley Graphs ◽  
Regular Maps ◽  
Cayley Maps

On Automorphism Groups of Symmetric Cayley Graphs of Finite Simple Groups with Valency Six

2010 ◽  
Vol 17 (01) ◽  
pp. 161-172
Author(s):  
Xingui Fang ◽  
Pu Niu ◽  
Jie Wang
Keyword(s):  
Automorphism Groups ◽  
Cayley Graphs ◽  
Simple Groups ◽  
Finite Simple Groups

In this paper we investigate the full automorphism groups of six-valent symmetric Cayley graphs Γ = Cay (G,S) for finite non-abelian simple groups G. We prove that for most finite non-abelian simple groups G, if Γ contains no cycle of length 4, then Aut Γ = G · Aut (G,S), where Aut (G,S) ≤ S 6.

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