Integral graph
In the mathematical field of graph theory, an integral graph is a graph whose spectrum consist 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[1].
Examples
- All the complete graphs are integral.
- Among the cubics symmetric graphs the utility graph, the Petersen 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.
References
- ^ 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.