Consistent Cycles in 1/2-Arc-Transitive Graphs ## AbstractA directed cycle C of a graph is called 1 k -consistent if there exists an automor- phism of the graph which acts as a k-step rotation of C. These cycles have previously been considered by several authors in the context of arc-transitive graphs. In this paper we extend these results to the case of graphs which are vertex-transitive, edge-transitive but not arc-transitive.
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