Characterizing finite locally s-arc transitive graphs with a star normal quotient

Abstract We characterize seven valent symmetric graphs of order 2 p q n 2p{q}^{n} with p < q p\lt q odd primes, extending a few previous results. Moreover, a consequence partially generalizes the result of Conder, Li and Potočnik [On the orders of arc-transitive graphs, J. Algebra 421 (2015), 167–186].

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Semiregular Automorphisms of Cubic Vertex-Transitive Graphs and the Abelian Normal Quotient Method

The Electronic Journal of Combinatorics ◽

10.37236/4842 ◽

2015 ◽

Vol 22 (3) ◽

Cited By ~ 1

Author(s):

Joy Morris ◽

Pablo Spiga ◽

Gabriel Verret

Keyword(s):

Transitive Group ◽

Cubic Graphs ◽

Cubic Graph ◽

Maximum Order ◽

Abelian Normal Subgroup ◽

Group Of Automorphisms ◽

Normal Quotient ◽

Vertex Transitive ◽

Vertex Transitive Graphs ◽

Transitive Graphs

We characterise connected cubic graphs admitting a vertex-transitive group of automorphisms with an abelian normal subgroup that is not semiregular. We illustrate the utility of this result by using it to prove that the order of a semiregular subgroup of maximum order in a vertex-transitive group of automorphisms of a connected cubic graph grows with the order of the graph.

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Trivalent Non-symmetric Vertex-Transitive Graphs of Order at Most 150

Algebra Colloquium ◽

10.1142/s1005386708000370 ◽

2008 ◽

Vol 15 (03) ◽

pp. 379-390 ◽

Cited By ~ 1

Author(s):

Xuesong Ma ◽

Ruji Wang

Keyword(s):

Automorphism Group ◽

Bipartite Graphs ◽

Type Ii ◽

Symmetric Graph ◽

Trivalent Graph ◽

Block Graphs ◽

Group A ◽

Vertex Transitive ◽

Vertex Transitive Graphs ◽

Transitive Graphs

Let X be a simple undirected connected trivalent graph. Then X is said to be a trivalent non-symmetric graph of type (II) if its automorphism group A = Aut (X) acts transitively on the vertices and the vertex-stabilizer Av of any vertex v has two orbits on the neighborhood of v. In this paper, such graphs of order at most 150 with the basic cycles of prime length are investigated, and a classification is given for such graphs which are non-Cayley graphs, whose block graphs induced by the basic cycles are non-bipartite graphs.

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