Integral graph

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In the mathematical field of graph theory, an integral graph is a graph whose adjacency matrix's spectrum consists entirely of integers. In other words, a graph is an integral graph if all of the roots of the characteristic polynomial of its adjacency matrix are integers.[1]

The notion was introduced in 1974 by Harary and Schwenk.[2]



  1. ^ Weisstein, Eric W. "Integral Graph". MathWorld.
  2. ^ 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.
  3. ^ Sander, Torsten (2009), "Sudoku graphs are integral", Electronic Journal of Combinatorics, 16 (1): Note 25, 7, MR 2529816