On Finite 2-Path-Transitive Graphs
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: 225237, 2013
2-path-transitivity symmetric graphs half-transitive graphs