Eigenvalue multiplicity in cubic signed graphs

Abstract Let G ˙ be a connected cubic signed graph of order n with μ as an eigenvalue of multiplicity k, and let t = n − k . In this paper, we prove that (i). if μ ∉ { − 1 , 0 , 1 } then k ≤ 1 2 n with equality if and only if μ = ± 3 , G ˙ is switching isomorphic to the cube with all negative quadrangles; ( i i ) . if μ = − 1 (resp., μ = 1 ) then k ≤ 1 2 n + 1 with equality if and only if G ˙ is switching isomorphic to ( K 4 , + ) (resp. ( K 4 , − ) ); ( i i i ) . if μ = 0 then k ≤ 1 2 n + 1 with equality if and only if G ˙ is switching isomorphic to ( K 3 , 3 , + ) .