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In the mathematical field of graph theory, an integral graph is a graph whose spectrum consists entirely of integers. In other words, a graph is an integral graph if all of the roots of its characteristic polynomial are integers.
- The complete graph Kn 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.