A graph 
is locally Petersen if, for each point 
of 
, the graph induced by 
on all points adjacent to 
(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 (Hall 1980).
 | symbol | graph | intersection array |
| 21 |  |  -Kneser graph |  |
| 63 |  | Conway-Smith graph |  |
| 65 |  | Hall graph |  |
