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Livingstone graph : ウィキペディア英語版
Livingstone graph

In the mathematical field of graph theory, the Livingstone graph is a distance-transitive graph with 266 vertices and 1463 edges. It is the largest distance-transitive graph with degree 11.
== Algebraic properties ==

The automorphism group of the Livingstone graph is the sporadic simple group J1, and the stabiliser of a point is PSL(2,11). As the stabiliser is maximal in J1, it acts primitively on the graph.
As the Livingstone graph is distance-transitive, PSL(2,11) acts transitively on the set of 11 vertices adjacent to a reference vertex ''v'', and also on the set of 12 vertices at distance 4 from ''v''. The second action is equivalent to the standard action of PSL(2,11) on the projective line over F11; the first is equivalent to an exceptional action on 11 points, related to the Paley biplane.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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