scholarly journals An infinite family of cubic nonnormal Cayley graphs on nonabelian simple groups

2018 ◽  
Vol 341 (5) ◽  
pp. 1282-1293
Author(s):  
Jiyong Chen ◽  
Binzhou Xia ◽  
Jin-Xin Zhou
Keyword(s):  
Cayley Graphs ◽  
Infinite Family ◽  
Simple Groups

scholarly journals A Family of Half-Transitive Graphs

10.37236/3140 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Jing Chen ◽  
Cai Heng Li ◽  
Ákos Seress
Keyword(s):  
Cayley Graphs ◽  
Infinite Family ◽  
Transitive Graphs

We construct an infinite family of half-transitive graphs, which contains infinitely many Cayley graphs, and infinitely many non-Cayley graphs.

SELF-COMPLEMENTARY VERTEX-TRANSITIVE GRAPHS NEED NOT BE CAYLEY GRAPHS

2001 ◽  
Vol 33 (6) ◽  
pp. 653-661 ◽  
Author(s):  
CAI HENG LI ◽  
CHERYL E. PRAEGER
Keyword(s):  
Wreath Product ◽  
Cayley Graphs ◽  
Infinite Family ◽  
Permutation Groups ◽  
General Study ◽  
Product Action ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs

A construction is given of an infinite family of finite self-complementary, vertex-transitive graphs which are not Cayley graphs. To the authors' knowledge, these are the first known examples of such graphs. The nature of the construction was suggested by a general study of the structure of self-complementary, vertex-transitive graphs. It involves the product action of a wreath product of permutation groups.

scholarly journals Non-expander Cayley Graphs of Simple Groups

2015 ◽  
Vol 43 (3) ◽  
pp. 1156-1175
Author(s):  
Gábor Somlai
Keyword(s):  
Cayley Graphs ◽  
Simple Groups

scholarly journals Arc-transitive Cayley graphs on nonabelian simple groups with prime valency

2021 ◽  
Vol 177 ◽  
pp. 105303
Author(s):  
Fu-Gang Yin ◽  
Yan-Quan Feng ◽  
Jin-Xin Zhou ◽  
Shan-Shan Chen
Keyword(s):  
Cayley Graphs ◽  
Simple Groups

A 2-ARC TRANSITIVE PENTAVALENT CAYLEY GRAPH OF 

2016 ◽  
Vol 93 (3) ◽  
pp. 441-446 ◽  
Author(s):  
BO LING ◽  
BEN GONG LOU
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Cayley Graphs ◽  
Discrete Math ◽  
Simple Groups ◽  
Alternating Group ◽  
Full Automorphism Group ◽  
Symmetric Graphs

Zhou and Feng [‘On symmetric graphs of valency five’, Discrete Math. 310 (2010), 1725–1732] proved that all connected pentavalent 1-transitive Cayley graphs of finite nonabelian simple groups are normal. We construct an example of a nonnormal 2-arc transitive pentavalent symmetric Cayley graph on the alternating group $\text{A}_{39}$. Furthermore, we show that the full automorphism group of this graph is isomorphic to the alternating group $\text{A}_{40}$.

scholarly journals Isospectral Cayley graphs of some finite simple groups

2006 ◽  
Vol 135 (2) ◽  
pp. 381-393 ◽  
Author(s):  
Alexander Lubotzky ◽  
Beth Samuels ◽  
Uzi Vishne
Keyword(s):  
Cayley Graphs ◽  
Simple Groups ◽  
Finite Simple Groups

Connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups

2009 ◽  
Vol 52 (2) ◽  
pp. 381-388
Author(s):  
ShangJin Xu ◽  
ZhengFei Wu ◽  
YunPing Deng
Keyword(s):  
Cayley Graphs ◽  
Simple Groups

scholarly journals Tetravalent 2-arc-transitive Cayley graphs on non-abelian simple groups

2019 ◽  
Vol 47 (11) ◽  
pp. 4565-4574 ◽  
Author(s):  
Jia-Li Du ◽  
Yan-Quan Feng
Keyword(s):  
Cayley Graphs ◽  
Simple Groups
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