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Distance-transitive graph
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<p>In the <a href="/facts/Mathematics/pxTouaz4">mathematical</a> field of <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a>, a distance-transitive graph is a <a href="/facts/Graph_(discrete_mathematics)/kw3eIBUe">graph</a> such that, given any two <a href="/facts/Vertex_(graph_theory)/WhlWmL3o">vertices</a> v and w at any <a href="/facts/Distance_(graph_theory)/EmQFKvqa">distance</a> i, and any other two vertices x and y at the same distance, there is an <a href="/facts/Graph_automorphism/If8FTdFE">automorphism</a> of the graph that carries v to x and w to y. Distance-transitive graphs were first defined in 1971 by <a href="/facts/Norman_L._Biggs/PXXEVgPP">Norman L. Biggs</a> and D. H. Smith. </p><p>A distance-transitive graph is interesting partly because it has a large <a href="/facts/Automorphism_group/65vImKwe">automorphism group</a>. Some interesting <a href="/facts/Finite_group/vv2tvogB">finite groups</a> are the automorphism groups of distance-transitive graphs, especially of those whose <a href="/facts/Diameter_(graph_theory)/EmQFKvqa">diameter</a> is 2. </p>