scholarly journals Most primitive groups are full automorphism groups of edge-transitive hypergraphs

2015 ◽  
Vol 421 ◽  
pp. 512-523 ◽  
Author(s):  
László Babai ◽  
Peter J. Cameron
Keyword(s):  
Automorphism Groups ◽  
Primitive Groups ◽  
Edge Transitive

scholarly journals On Edge-Transitive Graphs of Square-Free Order

10.37236/4573 ◽  
2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Cai Heng Li ◽  
Zai Ping Lu ◽  
Gai Xia Wang
Keyword(s):  
Automorphism Groups ◽  
Edge Transitive ◽  
Transitive Graphs ◽  
Free Order

We study the class of  edge-transitive graphs of square-free order and valency at most $k$. It is shown that, except for a few special families of graphs, only finitely many members in this class are basic (namely, not a normal multicover of another member). Using this result, we determine the automorphism groups of locally primitive arc-transitive graphs with square-free order.

Some semisymmetric graphs arising from finite vector spaces

2019 ◽  
Vol 19 (11) ◽  
pp. 2050216
Author(s):  
H. Y. Chen ◽  
H. Han ◽  
Z. P. Lu
Keyword(s):  
Finite Fields ◽  
Automorphism Groups ◽  
Bipartite Graphs ◽  
Vector Spaces ◽  
Finite Vector ◽  
Semisymmetric Graphs ◽  
Edge Transitive ◽  
Finite Vector Spaces

A graph is worthy if no two vertices have the same neighborhood. In this paper, we characterize the automorphism groups of unworthy edge-transitive bipartite graphs, and present some worthy semisymmetric graphs arising from vector spaces over finite fields. We also determine the automorphism groups of these graphs.

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.

On quasiprimitive edge-transitive graphs of odd order and twice prime valency

2020 ◽  
Vol 23 (6) ◽  
pp. 1017-1037
Author(s):  
Hong Ci Liao ◽  
Jing Jian Li ◽  
Zai Ping Lu
Keyword(s):  
Automorphism Group ◽  
Connected Graph ◽  
Automorphism Groups ◽  
Primitive Group ◽  
Odd Order ◽  
Vertex Set ◽  
Edge Transitive ◽  
Affine Type ◽  
Transitive Graphs

AbstractA graph is edge-transitive if its automorphism group acts transitively on the edge set. In this paper, we investigate the automorphism groups of edge-transitive graphs of odd order and twice prime valency. Let {\varGamma} be a connected graph of odd order and twice prime valency, and let G be a subgroup of the automorphism group of {\varGamma}. In the case where G acts transitively on the edge set and quasiprimitively on the vertex set of {\varGamma}, we prove that either G is almost simple, or G is a primitive group of affine type. If further G is an almost simple primitive group, then, with two exceptions, the socle of G acts transitively on the edge set of {\varGamma}.

Automorphism Groups of Bouwer Graphs

2018 ◽  
Vol 25 (03) ◽  
pp. 493-508 ◽  
Author(s):  
Mimi Zhang ◽  
Jinxin Zhou
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Transitive Graph ◽  
Full Automorphism Group ◽  
Vertex Set ◽  
Edge Transitive ◽  
Positive Integers

Let k, m and n be three positive integers such that 2m ≡ 1 (mod n) and k ≥ 2. The Bouwer graph, which is denoted by B(k, m, n), is the graph with vertex set [Formula: see text] and two vertices being adjacent if they can be written as (a, b) and (a + 1, c), where either c = b or [Formula: see text] differs from [Formula: see text] in exactly one position, say the jth position, where [Formula: see text]. Every B(k, m, n) is a vertex- and edge-transitive graph, and Bouwer proved that B(k, 6, 9) is half-arc-transitive for every k ≥ 2. In 2016, Conder and Žitnik gave the classification of half-arc-transitive Bouwer graphs. In this paper, the full automorphism group of every B(k, m, n) is determined.

scholarly journals The automorphism groups of non-edge-transitive rose window graphs

2014 ◽  
Vol 9 (1) ◽  
pp. 63-75 ◽  
Author(s):  
Ted Dobson ◽  
István Kovács ◽  
Štefko Miklavič
Keyword(s):  
Automorphism Groups ◽  
Edge Transitive
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