[1] It is a rank 3 strongly regular graph with parameters (100,36,14,12) and a maximum coclique of size 10.

This parameter set is not unique, it is however uniquely determined by its parameters as a rank 3 graph.

The Hall–Janko graph was originally constructed by D. Wales to establish the existence of the Hall-Janko group as an index 2 subgroup of its automorphism group.

The Hall–Janko graph can be constructed out of objects in U3(3), the simple group of order 6048:[2][3] The characteristic polynomial of the Hall–Janko graph is

Therefore the Hall–Janko graph is an integral graph: its spectrum consists entirely of integers.