• Corpus ID: 254044091

Two-arc-transitive bicirculants

  title={Two-arc-transitive bicirculants},
  author={Wei Jin},
  • W. Jin
  • Published 26 November 2022
  • Mathematics
. In this paper, we determine the class of finite 2-arc-transitive bicirculants. We show that a connected 2-arc-transitive bicirculant is one of the following graphs: C 2 n where n > 2, K 2 n where n > 2, K n,n where n > 3, K n,n − n K 2 where n > 4, B (PG( d − 1 , q )) and B ′ (PG( d − 1 , q )) where d ≥ 3 and q is a prime power, X 1 (4 , q ) where q ≡ 3 (mod 4) is a prime power, K 2 d q +1 where q is an odd prime power and d ≥ 2 dividing q − 1, AT Q (1 + q, 2 d ) where d | q − 1 and d ∤ 1 2… 

Tables from this paper



Classification of 2-arc-transitive dihedrants

A classification of pentavalent arc-transitive bicirculants

A bicirculant is a graph admitting an automorphism with two cycles of equal length in its cycle decomposition. A graph is said to be arc-transitive if its automorphism group acts transitively on the

2-Arc-transitive cyclic covers of Kn,n−nK2

Du et al. (in J. Comb. Theory B 74:276–290, 1998 and J. Comb. Theory B 93:73–93, 2005), classified regular covers of complete graph whose fiber-preserving automorphism group acts 2-arc-transitively,

On Finite Affine 2-Arc Transitive Graphs

This paper gives a classification of all primitive affine 2-arc transitive graphs, and all finite 'bi-primitive' affine 1-arctransitive graphs such that the stabilizer of the bipartition of the vertices is primitive on each part of the antipartition.

Strongly Regular Semi-Cayley Graphs

We consider strongly regular graphs Γ = (V, E) on an even number, say 2n, of vertices which admit an automorphism group G of order n which has two orbits on V. Such graphs will be called strongly

On non-normal arc-transitive 4-valent dihedrants

Let X be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group Dn such that X is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within

Locally s‐distance transitive graphs

It is proved that, for s � 2, a nondegenerate, nonbasic graph in the class is either a complete multipartite graph, or a normal cover of a basic graph, and that, apart from the complete bipartite graphs, each basic graph admits a faithful quasiprimitive action on each of its (1 or 2) vertex orbits.

Finite Permutation Groups

Classification of Symmetric Tabačjn Graphs

The Tabačjn graphs are introduced, a family of pentavalent bicirculants which are a natural generalization of generalized Petersen graphs obtained from them by adding two additional perfect matchings between the two orbits of a semiregular automorphism.

2-Walk-Regular Dihedrants from Group-Divisible Designs

This note constructs bipartite 2-walk-regular graphs with exactly 6 distinct eigenvalues as incidence graphs of group-divisible designs with the dual property, and shows that they are 2-arc-transitive dihedrants.