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.[1]

Livingstone graph
Vertices266
Edges1463
Radius4
Diameter4
Girth5
Automorphisms175560 (J1)
PropertiesSymmetric
Distance-transitive
Primitive
Table of graphs and parameters

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.

gollark: That sounds exactly like what TJ09 would do.
gollark: They shall pile up forever. I consider myself relatively good at cave hunting, and I have piles of xenowyrms anyway.
gollark: (honestly, I doubt TJ09 bothered to cap the prices)
gollark: Okay then, a few possibilities:* the pricing does **not** adjust very fast, so people with enough shards will get them quickly, then the price will skyrocket after the first group do* the pricing does adjust fast, so the price climbs 100 shards a week and a few lucky people get them each week* either of those, but the price is capped somehow so it doesn't climb massively
gollark: No, 1312.

References
  1. Weisstein, Eric W. "Livingstone Graph". MathWorld.


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