Eigenvalue multiplicity in cubic signed graphs

Let (G) over dot be a connected cubic signed graph of order nwith mu as an eigenvalue of multiplicity k, and let t = n - k. In this paper, we prove that (i). if mu is not an element of{-1, 0, 1} then k <= 1/2n with equality if and only if mu = +/-root 3, (G) over dot is switching isomorphic to the cube with all negative quadrangles; (ii). if mu = -1(resp(+), mu = 1) then k <= 1/2n + 1 with equality if and only if (G) over dot is switching isomorphic to (K-4, +)(resp. (K-4, -)); (iii). if mu = 0 then k <= 1/2n + 1 with equality if and only if (G) over dot is switching isomorphic to (K-3,K-3, +). (C) 2021 Elsevier Inc. All rights reserved.