Distance-transitive graph

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In mathematics, a distance-transitive graph is a graph (mathematics) such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y.

A distance transitive graph is vertex transitive and arc transitive as well as distance regular.

A distance-transitive graph is interesting partly because it has a large automorphism group. Some interesting finite groups are the automorphism groups of distance-transitive graphs, especially of those whose diameter is 2.


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