Spectral numbers related to signed graphs

Abstract

We prove that {-2, - √2,-1,0,1, √2,2} is the set of all real numbers ρ such that the following holds: if ρ is not less than the least eigenvalue of a signed graph S and not larger than the largest eigenvalue of S, then an eigenvalue of one of the subgraphs of S is equal to ρ. We also derive some variants of this result.