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 Frank Harary and Allen Schwenk.[2]

  1. ^ Weisstein, Eric W., "Integral Graph", MathWorld
  2. ^ Harary, Frank; Schwenk, Allen J. (1974), "Which graphs have integral spectra?", in Bari, Ruth A.; Harary, Frank (eds.), Graphs and Combinatorics: Proceedings of the Capital Conference on Graph Theory and Combinatorics at the George Washington University, Washington, D.C., June 18–22, 1973, Lecture Notes in Mathematics, vol. 406, Springer, pp. 45–51, doi:10.1007/BFb0066434, MR 0387124