scholarly journals Arc-Transitive Dihedral Regular Covers of Cubic Graphs

10.37236/4035 ◽  
2014 ◽  
Vol 21 (3) ◽  
Author(s):  
Jicheng Ma
Keyword(s):  
Transformation Group ◽  
Petersen Graph ◽  
Cubic Graphs ◽  
Regular Covering ◽  
Symmetric Graphs ◽  
Cyclic Covers ◽  
Covering Projection

A regular covering projection is called dihedral or abelian if the covering transformation group is dihedral or abelian. A lot of work has been done with regard to the classification of arc-transitive abelian (or elementary abelian, or cyclic) covers of symmetric graphs. In this paper, we investigate arc-transitive dihedral regular covers of symmetric (arc-transitive) cubic graphs. In particular, we classify all arc-transitive dihedral regular covers of $K_4$, $K_{3,3}$, the 3-cube $Q_3$ and the Petersen graph.

Arc-transitive abelian regular covering graphs

2016 ◽  
Vol 26 (07) ◽  
pp. 1369-1393 ◽  
Author(s):  
Jicheng Ma
Keyword(s):  
Complete Graph ◽  
Abelian Groups ◽  
Cubic Graphs ◽  
New Approach ◽  
Regular Covering ◽  
Symmetric Graphs

A lot of attention has been paid recently to the construction of symmetric covers of symmetric graphs. After a new approach given by Conder and the author [Arc-transitive abelian regular covers of cubic graphs, J. Algebra 387 (2013) 215–242], the group of covering transformations can be extended to more general abelian groups rather than cyclic or elementary abelian groups. In this paper, by using the Conder–Ma approach, we investigate the symmetric covers of 4-valent symmetric graphs. As an application, all the arc-transitive abelian regular covers of the 4-valent complete graph [Formula: see text] which can be obtained by lifting the arc-transitive subgroups of automorphisms [Formula: see text] and [Formula: see text] are classified.

2-ARC-TRANSITIVE REGULAR COVERS OF HAVING THE COVERING TRANSFORMATION GROUP

2016 ◽  
Vol 101 (2) ◽  
pp. 145-170 ◽  
Author(s):  
SHAOFEI DU ◽  
WENQIN XU
Keyword(s):  
Automorphism Group ◽  
Bipartite Graph ◽  
Transformation Group ◽  
Complete Bipartite Graph ◽  
Cyclic Covers ◽  
Acts 2

This paper contributes to the regular covers of a complete bipartite graph minus a matching, denoted $K_{n,n}-nK_{2}$, whose fiber-preserving automorphism group acts 2-arc-transitively. All such covers, when the covering transformation group $K$ is either cyclic or $\mathbb{Z}_{p}^{2}$ with $p$ a prime, have been determined in Xu and Du [‘2-arc-transitive cyclic covers of $K_{n,n}-nK_{2}$’, J. Algebraic Combin.39 (2014), 883–902] and Xu et al. [‘2-arc-transitive regular covers of $K_{n,n}-nK_{2}$ with the covering transformation group $\mathbb{Z}_{p}^{2}$’, Ars. Math. Contemp.10 (2016), 269–280]. Finally, this paper gives a classification of all such covers for $K\cong \mathbb{Z}_{p}^{3}$ with $p$ a prime.

scholarly journals Cubic symmetric graphs of order twice an odd prime-power

2006 ◽  
Vol 81 (2) ◽  
pp. 153-164 ◽  
Author(s):  
Yan-Quan Feng ◽  
Jin Ho Kwak
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Prime Power ◽  
Symmetric Graph ◽  
Cubic Graphs ◽  
Full Automorphism Group ◽  
Symmetric Graphs ◽  
Regular Subgroup

AbstractAn automorphism group of a graph is said to be s-regular if it acts regularly on the set of s-arcs in the graph. A graph is s-regular if its full automorphism group is s-regular. For a connected cubic symmetric graph X of order 2pn for an odd prime p, we show that if p ≠ 5, 7 then every Sylow p-subgroup of the full automorphism group Aut(X) of X is normal, and if p ≠3 then every s-regular subgroup of Aut(X) having a normal Sylow p-subgroup contains an (s − 1)-regular subgroup for each 1 ≦ s ≦ 5. As an application, we show that every connected cubic symmetric graph of order 2pn is a Cayley graph if p > 5 and we classify the s-regular cubic graphs of order 2p2 for each 1≦ s≦ 5 and each prime p. as a continuation of the authors' classification of 1-regular cubic graphs of order 2p2. The same classification of those of order 2p is also done.

A classification of cubic symmetric graphs of order 16p 2

2011 ◽  
Vol 121 (3) ◽  
pp. 249-257
Author(s):  
MEHDI ALAEIYAN ◽  
B N ONAGH ◽  
M K HOSSEINIPOOR
Keyword(s):  
Symmetric Graphs

scholarly journals Unitary graphs and classification of a family of symmetric graphs with complete quotients

2013 ◽  
Vol 38 (3) ◽  
pp. 745-765 ◽  
Author(s):  
Massimo Giulietti ◽  
Stefano Marcugini ◽  
Fernanda Pambianco ◽  
Sanming Zhou
Keyword(s):  
Symmetric Graphs

scholarly journals A Classification of Symmetric Graphs of Order 3p

1993 ◽  
Vol 58 (2) ◽  
pp. 197-216 ◽  
Author(s):  
R.J. Wang ◽  
M.Y. Xu
Keyword(s):  
Symmetric Graphs

Pentavalent Symmetric Graphs of Order Twice a Prime Square

2015 ◽  
Vol 22 (03) ◽  
pp. 383-394 ◽  
Author(s):  
Jiangmin Pan ◽  
Zhe Liu ◽  
Xiaofen Yu
Keyword(s):  
Double Cover ◽  
Split Extension ◽  
Special Group ◽  
Cayley Digraph ◽  
Symmetric Graphs ◽  
Coset Graph

A classification of pentavalent symmetric graphs of order twice a prime square is given. It is proved that such a graph is a coset graph of ℤ3. A 6 (non-split extension), or a bi-coset graph of an extra-special group of order 125, or the standard double cover of a specific abelian Cayley digraph of order a prime square.

scholarly journals Classification of 4- and 5-arc-transitive cubic graphs of small girth: corrigendum

1992 ◽  
Vol 52 (3) ◽  
pp. 419-420
Author(s):  
Margaret J. Morton
Keyword(s):  
Cubic Graphs ◽  
Regular Group ◽  
Group Of Automorphisms ◽  
Transitive Graphs

The purpose of this brief note is to point out an omission, at the top of page 145, in my paper [1]. Richard Weiss has kindly pointed out that there exist 5-arc-transitive graphs with no 4-arc regular group of automorphisms.

Classification of the Blaschke Isoparametric Hypersurfaces in Lorentzian Space Forms

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
Fengyun Zhang ◽  
Huafei Sun
Keyword(s):  
Conformal Transformation ◽  
Transformation Group ◽  
Second Fundamental Form ◽  
Conformal Metric ◽  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Lorentzian Space ◽  
Blaschke Tensor ◽  
Lorentzian Space Forms

AbstractIn this paper, we study regular immersed hypersurfaces in Lorentzian space forms with a conformal metric, a conformal second fundamental form, the conformal Blaschke tensor and a conformal form, which are invariants under the conformal transformation group. We classify all the immersed hypersurfaces in Lorentzian space forms with two distinct constant Blaschke eigenvalues and vanishing conformal form.

Edge-transitive dihedral or cyclic covers of cubic symmetric graphs of order 2P

COMBINATORICA ◽  
2014 ◽  
Vol 34 (1) ◽  
pp. 115-128 ◽  
Author(s):  
Jin-Xin Zhou ◽  
Yan-Quan Feng
Keyword(s):  
Symmetric Graphs ◽  
Cyclic Covers ◽  
Edge Transitive
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