Integral graph

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]

Examples

References

  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. 4551, 1974.
  3. Sander, Torsten (2009), "Sudoku graphs are integral", Electronic Journal of Combinatorics, 16 (1): Note 25, 7, MR 2529816
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