Primitivity and ends of graphs

Abstract

A graphX is said to beprimitive if its automorphism groupG acts primitively on the vertex setVX; that is, the onlyG-invariant equivalence relations onVX are the one where all the classes have size one and the equivalence relation which has only one class, the whole ofVX. 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.

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Möller, R.G. Primitivity and ends of graphs. Combinatorica 14, 477–484 (1994). https://doi.org/10.1007/BF01302968

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AMS subject classification code (1991)

  • 05 C 25
  • 20 B 15
  • 20 B 27