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{\bf Marko Boben, \v{S}tefko Miklavi\v{c} and Primo\v z Poto\v cnik }
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{\bf Consistent Cycles in $1\over2$-Arc-Transitive Graphs}
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A directed cycle $C$ of a graph is called $1\over k$-consistent if there
exists an automorphism 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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