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On the Automorphism Groups of Cayley Graphs of Finite Simple Groups
Author(s) -
Fang Xin Gui,
Praeger Cheryl E.,
Wang Jie
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003666
Subject(s) - cayley graph , mathematics , simple group , classification of finite simple groups , valency , combinatorics , simple (philosophy) , automorphism , transitive relation , group of lie type , vertex transitive graph , automorphism group , cayley's theorem , outer automorphism group , discrete mathematics , graph , group theory , pure mathematics , voltage graph , line graph , philosophy , linguistics , epistemology
Let G be a finite nonabelian simple group and let Γ be a connected undirected Cayley graph for G . The possible structures for the full automorphism group AutΓ are specified. Then, for certain finite simple groups G , a sufficient condition is given under which G is a normal subgroup of AutΓ. Finally, as an application of these results, several new half‐transitive graphs are constructed. Some of these involve the sporadic simple groups G = J 1 , J 4 , Ly and BM, while others fall into two infinite families and involve the Ree simple groups and alternating groups. The two infinite families contain examples of half‐transitive graphs of arbitrarily large valency.