= Distance-transitive action on a graph
= Distance transitivity
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= Distance-transitively
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A subgroup of the <graph automorphism> group acts distance-transitively when it is <transitive> on the <ordered pairs> of <vertices> at each fixed <graph distance>. Thus two vertex pairs at the same distance can be matched by one automorphism from that subgroup. Existence of such a subgroup implies that the full automorphism group has the same property, making the graph a <distance-transitive graph>. The specified subgroup need not be the entire automorphism group.
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