In the mathematical field of graph theory, the Hall–Janko graph, also known as the Hall-Janko-Wales graph, is a 36-regular undirected graph with 100 vertices and 1800 edges. 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: The characteristic polynomial of the Hall–Janko graph is. Therefore the Hall–Janko graph is an integral graph: its spectrum consists entirely of integers.