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primitive graphs
Cayley graphs of the group ?4 that are limits of minimal vertex-primitive graphs of type HA
      
In the joint paper by Giudici, Li, Praeger, Seress, and Trofimov, it is proved that any graph that is a limit of vertex-primitive graphs of type HA is isomorphic to a Cayley graph of the group ?d.
      
Earlier, the author proved that for d ≤ 3 the number of pairwise nonisomorphic Cayley graphs of the group ?d, which are limits of minimal vertex-primitive graphs of type HA, is finite (and obtained their explicit description).
      
The connectivities of locally finite primitive graphs
      
We investigate the end structure of locally finite primitive graphs.
      
Our main result shows that it has a very simple description; in particular, locally finite primitive graphs are accessible in the sense of Thomassen and Woess.
      
We give a version of Derek Smith's famous theorem for reducing the classification of distance-regular graphs to that of primitive graphs.
      
The Cayley graphs of ?d and the limits of vertex-primitive graphs of HA-type
      
In addition, for d >amp;lt; 4 we list all Cayley graphs of ?d that are limits of minimal vertex-primitive graphs.
      
 

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