One-factorizations of complete graphs with vertex-regular automorphism groups

2001 ◽  
Vol 10 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Arrigo Bonisoli ◽  
Domenico Labbate
Keyword(s):  
Automorphism Groups ◽  
Complete Graphs ◽  
Regular Automorphism

On infinite tournaments with regular automorphism groups

1981 ◽  
Vol 22 (1) ◽  
pp. 46-53
Author(s):  
D. A. Holton ◽  
Mark E. Watkins
Keyword(s):  
Automorphism Groups ◽  
Regular Automorphism

Infinite quasigroups with given regular automorphism groups

1978 ◽  
Vol 8 (1) ◽  
pp. 310-319 ◽  
Author(s):  
L. Babai ◽  
P. Frankl
Keyword(s):  
Automorphism Groups ◽  
Regular Automorphism

scholarly journals ON A CLASS OF EDGE-TRANSITIVE DISTANCE-REGULAR ANTIPODAL COVERS OF COMPLETE GRAPHS

2021 ◽  
Vol 7 (2) ◽  
pp. 136
Author(s):  
Ludmila Yu. Tsiovkina
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Satisfying Condition ◽  
Complete Graphs ◽  
Transitive Graph ◽  
Common Neighbour ◽  
Moore Graph ◽  
Antipodal Cover ◽  
Edge Transitive

The paper is devoted to the problem of classification of edge-transitive distance-regular antipodal covers of complete graphs. This extends the classification of those covers that are arc-transitive, which has been settled except for some tricky cases that remain to be considered, including the case of covers satisfying condition \(c_2=1\) (which means that every two vertices at distance 2  have exactly one common neighbour).Here it is shown that an edge-transitive distance-regular antipodal cover of a complete graph with \(c_2=1\) is either the second neighbourhood of a vertex in a Moore graph of valency 3 or 7, or a Mathon graph, or a half-transitive graph whose automorphism group induces an affine  \(2\)-homogeneous group on the set of its fibres. Moreover,  distance-regular  antipodal covers of complete graphs  with \(c_2=1\) that admit  an automorphism group acting  \(2\)-homogeneously on the set of fibres (which turns out to be an approximation of the property of edge-transitivity  of such  cover), are described.   A well-known correspondence between distance-regular antipodal covers of complete graphs with \(c_2=1\) and geodetic graphs of diameter two that can be viewed as underlying graphs of certain Moore geometries, allows us to effectively restrict admissible automorphism groups of covers under consideration by combining Kantor's classification of involutory automorphisms of these geometries together with the classification of finite 2-homogeneous permutation groups.

Sign in / Sign up

Export Citation Format

Share Document