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integral graph
In the mathematical field of graph theory, an integral graph is a graph whose spectrum consists entirely of integers. In other words, a graphs is an integral graph if all the eigenvalues of its characteristic polynomial are integers.
The notion was introduced in 1974 by Harary and Schwenk.〔Harary, F. and Schwenk, A. J. "Which Graphs have Integral Spectra?" In Graphs and Combinatorics (Ed. R. Bari and F. Harary). Berlin: Springer-Verlag, pp. 45–51, 1974.〕
==Examples==
*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.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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