Integral graph

Examples

• The complete graph K_n is integral for all n.
• The edgeless graph is integral for all n.
• Among the cubic symmetric graphs the utility graph, the Petersen graph, the Nauru graph and the Desargues graph are integral.
• The Higman–Sims graph, the Hall–Janko graph, the Clebsch graph, the Hoffman–Singleton graph, the Shrikhande graph and the Hoffman graph are integral.
• A regular graph is periodic if and only if it is an integral graph.
• A walk-regular graph that admits perfect state transfer is an integral graph.
• The Sudoku graphs, graphs whose vertices represent cells of a Sudoku board and whose edges represent cells that should not be equal, are integral.