A graph Γ is locally Petersen if, for each point t of Γ, the graph induced by Γ on all points adjacent to t (i.e., the neighborhood graph) is isomorphic to the Petersen graph. There are exactly three distinct locally Petersen graphs, as summarized in the following table. n | symbol | graph | intersection array 21 | Γ^(1) | (7, 2)-Kneser graph | {10, 6;1, 6} 63 | Γ^(2) | Conway-Smith graph | {10, 6, 4, 1;1, 2, 6, 10} 65 | Γ^(3) | Hall graph | {10, 6, 4;1, 2, 5}

Conway-Smith graph | Hall graph | Kneser graph | local graph | Petersen graph