|
|
| |
| $s$-REGULAR DIHEDRAL COVERINGS OF THE COMPLETE GRAPH OF ORDER 4 |
| |
Citation： |
FENG Yanquan,J. H. KWAK.$s$-REGULAR DIHEDRAL COVERINGS OF THE COMPLETE GRAPH OF ORDER 4[J].Chinese Annals of Mathematics B,2004,25(1):57~64 |
| Page view： 1062
Net amount： 756 |
Authors： |
FENG Yanquan; J. H. KWAK |
Foundation： |
Project supported by the Excellent Young Teachers Program of the Ministry of Education of China,
the National Natural Science Foundation of China, the Scientific Research Foundation for the Returned
Overseas Chinese Scholars, the Ministry of Education of China and the Com$^2$MaC-KOSEF in Korea. |
|
|
| Abstract： |
A graph is {$s$-regular} if its automorphism group acts regularly
on the set of its $s$-arcs. An infinite family of cubic
$1$-regular graphs was constructed in [7] as cyclic coverings of
the three-dimensional Hypercube, and a classification of all
$s$-regular cyclic coverings of the complete bipartite graph of
order $6$ was given in [8] for each $s\geq 1$, whose
fibre-preserving automorphism subgroups act arc-transitively. In
this paper, the authors classify all $s$-regular dihedral
coverings of the complete graph of order $4$ for each $s\geq 1$,
whose fibre-preserving automorphism subgroups act
arc-transitively. As a result, a new infinite family of cubic
$1$-regular graphs is constructed. |
Keywords： |
s-regular graphs, s-arc-transitive graphs, Regular coverings |
Classification： |
05C25, 20B25 |
|
|
Download PDF Full-Text
|
|
|
|
