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).

Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. §1.16.5 in Distance
Regular Graphs. New York: Springer-Verlag, p. 37, 1989.Hall,
J. I. "Locally Petersen Graphs." J. Graph Th.4, 173-187,
1980.