scholarly journals A note on the automorphism groups of cubic Cayley graphs of finite simple groups

2010 ◽  
Vol 310 (21) ◽  
pp. 3030-3032 ◽  
Author(s):  
Cui Zhang ◽  
Xin Gui Fang
Keyword(s):  
Automorphism Groups ◽  
Cayley Graphs ◽  
Simple Groups ◽  
Finite Simple Groups

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.

scholarly journals On Prime-Valent Symmetric Cayley Graphs of Finite Simple Groups

10.37236/9377 ◽  
2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Jing Jian Li ◽  
Jicheng Ma
Keyword(s):  
Automorphism Groups ◽  
Cayley Graphs ◽  
Simple Groups ◽  
Finite Simple Groups

We give a characterization of the automorphism groups of connected prime-valent  symmetric Cayley graphs on finite (non-abelian) simple groups.

On the Automorphism Groups of Cayley Graphs of Finite Simple Groups

2002 ◽  
Vol 66 (3) ◽  
pp. 563-578 ◽  
Author(s):  
Xin Gui Fang ◽  
Cheryl E. Praeger ◽  
Jie Wang
Keyword(s):  
Automorphism Groups ◽  
Cayley Graphs ◽  
Simple Groups ◽  
Finite Simple Groups

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

scholarly journals On isomorphisms of connected Cayley graphs, III

1998 ◽  
Vol 58 (1) ◽  
pp. 137-145 ◽  
Author(s):  
Cai Heng Li
Keyword(s):  
Finite Group ◽  
Positive Integer ◽  
Simple Group ◽  
Prime Divisor ◽  
Cayley Graphs ◽  
Simple Groups ◽  
Linear Groups ◽  
Finite Simple Groups ◽  
Natural Question ◽  
A Finite Group

For a finite group G and a subset S of G which does not contain the identity of G, we use Cay(G, S) to denote the Cayley graph of G with respect to S. For a positive integer m, the group G is called a (connected) m-DCI-group if for any (connected) Cayley graphs Cay(G, S) and Cay(G, T) of out-valency at most m, Sσ = T for some σ ∈ Aut(G) whenever Cay(G, S) ≅ Cay(G, T). Let p(G) be the smallest prime divisor of |G|. It was previously shown that each finite group G is a connected m-DCI-group for m ≤ p(G) − 1 but this is not necessarily true for m = p(G). This leads to a natural question: which groups G are connected p(G)-DCI-groups? Here we conjecture that the answer of this question is positive for finite simple groups, that is, finite simple groups are all connected 2-DCI-groups. We verify this conjecture for the linear groups PSL(2, q). Then we prove that a nonabelian simple group G is a 2-DCI-group if and only if G = A5.

scholarly journals 5-Arc transitive cubic Cayley graphs on finite simple groups

2007 ◽  
Vol 28 (3) ◽  
pp. 1023-1036 ◽  
Author(s):  
Shang Jin Xu ◽  
Xin Gui Fang ◽  
Jie Wang ◽  
Ming Yao Xu
Keyword(s):  
Cayley Graphs ◽  
Simple Groups ◽  
Finite Simple Groups

scholarly journals CLASSIFICATION OF TETRAVALENT -TRANSITIVE NONNORMAL CAYLEY GRAPHS OF FINITE SIMPLE GROUPS

2021 ◽  
pp. 1-9
Author(s):  
XIN GUI FANG ◽  
JIE WANG ◽  
SANMING ZHOU
Keyword(s):  
Automorphism Group ◽  
Simple Group ◽  
Cayley Graph ◽  
Finite Simple Group ◽  
Cayley Graphs ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Edge Transitive

Abstract A graph $\Gamma $ is called $(G, s)$ -arc-transitive if $G \le \text{Aut} (\Gamma )$ is transitive on the set of vertices of $\Gamma $ and the set of s-arcs of $\Gamma $ , where for an integer $s \ge 1$ an s-arc of $\Gamma $ is a sequence of $s+1$ vertices $(v_0,v_1,\ldots ,v_s)$ of $\Gamma $ such that $v_{i-1}$ and $v_i$ are adjacent for $1 \le i \le s$ and $v_{i-1}\ne v_{i+1}$ for $1 \le i \le s-1$ . A graph $\Gamma $ is called 2-transitive if it is $(\text{Aut} (\Gamma ), 2)$ -arc-transitive but not $(\text{Aut} (\Gamma ), 3)$ -arc-transitive. A Cayley graph $\Gamma $ of a group G is called normal if G is normal in $\text{Aut} (\Gamma )$ and nonnormal otherwise. Fang et al. [‘On edge transitive Cayley graphs of valency four’, European J. Combin.25 (2004), 1103–1116] proved that if $\Gamma $ is a tetravalent 2-transitive Cayley graph of a finite simple group G, then either $\Gamma $ is normal or G is one of the groups $\text{PSL}_2(11)$ , $\text{M} _{11}$ , $\text{M} _{23}$ and $A_{11}$ . However, it was unknown whether $\Gamma $ is normal when G is one of these four groups. We answer this question by proving that among these four groups only $\text{M} _{11}$ produces connected tetravalent 2-transitive nonnormal Cayley graphs. We prove further that there are exactly two such graphs which are nonisomorphic and both are determined in the paper. As a consequence, the automorphism group of any connected tetravalent 2-transitive Cayley graph of any finite simple group is determined.

scholarly journals On cubic Cayley graphs of finite simple groups

2002 ◽  
Vol 244 (1-3) ◽  
pp. 67-75 ◽  
Author(s):  
Xin Gui Fang ◽  
Cai Heng Li ◽  
Jie Wang ◽  
Ming Yao Xu
Keyword(s):  
Cayley Graphs ◽  
Simple Groups ◽  
Finite Simple Groups
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