quality:corruption, quality:correction
Integral classification

An integral graph is one whose eigenvalues are all integers. While the complete classification of integral graphs remains an open problem, the Cayley graphs of certain groups are always integral.Using previous characterizations of the spectrum of Cayley graphs, note that Γ (G, S) {\displaystyle \Gamma (G,S)} is integral iff the eigenvalues of ρ (S) {\displaystyle \rho (S)} are integral for every representation ρ {\displaystyle \rho } of G {\displaystyle G}.