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Keywords:

  • symmetric graphs;
  • half-transitive graphs;
  • 2-path-transitivity

Abstract

The class of graphs that are 2-path-transitive but not 2-arc-transitive is investigated. The amalgams for such graphs are determined, and structural information regarding the full automorphism groups is given. It is then proved that a graph is 2-path-transitive but not 2-arc-transitive if and only if its line graph is half-arc-transitive, thus providing a method for constructing new families of half-arc-transitive graphs. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 225–237, 2013