The Petersen line graph is the line graph of the Petersen graph. It is a 15-vertex, 30-edge quartic vertex-transitive graph, and is the graph Qt39.
It is a distance-regular graph (and distance-transitive graph) with diameter
3, intersection array 
, graph spectrum 
, and automorphism
group 
(DistanceRegular.org). It is also an antipodal graph.
The graph is nonplanar, but is toroidal and has graph crossing number 7. It is Hamiltonian with 160 Hamiltonian cycles.
The Petersen line graph is implemented in the Wolfram Language as GraphData["PetersenLineGraph"].
