Constructions of quasiprimitive two-arc transitive graphs of product action type

2001 ◽  
Vol 33 (6) ◽  
pp. 653-661 ◽  
Author(s):  
CAI HENG LI ◽  
CHERYL E. PRAEGER

A construction is given of an infinite family of finite self-complementary, vertex-transitive graphs which are not Cayley graphs. To the authors' knowledge, these are the first known examples of such graphs. The nature of the construction was suggested by a general study of the structure of self-complementary, vertex-transitive graphs. It involves the product action of a wreath product of permutation groups.


2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Qian Cai ◽  
Hua Zhang

Primitive permutation groups of prime power degree are known to be affine type, almost simple type, and product action type. At the present stage finding an explicit classification of primitive groups of affine type seems untractable, while the product action type can usually be reduced to almost simple type. In this paper, we present a short survey of the development of primitive groups of prime power degree, together with a brief description on such groups.


Author(s):  
CAI HENG LI ◽  
GUANG RAO ◽  
SHU JIAO SONG

Abstract Vertex-primitive self-complementary graphs were proved to be affine or in product action by Guralnick et al. [‘On orbital partitions and exceptionality of primitive permutation groups’, Trans. Amer. Math. Soc.356 (2004), 4857–4872]. The product action type is known in some sense. In this paper, we provide a generic construction for the affine case and several families of new self-complementary Cayley graphs are constructed.


Author(s):  
Michael P. DeJonge

If, as Chapter 12 argues, much of Bonhoeffer’s resistance thinking remains stable even as he undertakes the novel conspiratorial resistance, what is new in his resistance thinking in the third phase? What receives new theological elaboration is the resistance activity of the individual, which in the first two phases was overshadowed by the resistance role played by the church. Indeed, as this chapter shows, Bonhoeffer’s conspiratorial activity is associated with what he calls free responsible action (type 6), and this is the action of the individual, not the church, in the exercise of vocation. As such, the conspiratorial activity is most closely related to the previously developed type 1 resistance, which includes individual vocational action in response to state injustice. But the conspiratorial activity differs from type 1 resistance as individual vocational action in the extreme situation.


2008 ◽  
Vol 15 (03) ◽  
pp. 379-390 ◽  
Author(s):  
Xuesong Ma ◽  
Ruji Wang

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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