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≤12n with equality if and only if μ=±3, G˙ is switching isomorphic to the cube with all negative quadrangles;(ii).if μ=−1 (resp., μ=1) then k≤12n+1 with equality if and only if G˙ is switching isomorphic to (K4,+) (resp. (K4,−));(iii).if μ=0 then k≤12n+1 with equality if and only if G˙ is switching isomorphic to (K3,3,+).