The Nullity of Bicyclic Signed Graphs
Abstract
Let be a signed graph and let A() be the adjacency matrix of . The nullity of is the multiplicity of eigenvalue zero in the spectrum of A(). In this paper we characterize the signed graphs of order n with nullity n-2 or n-3, and introduce a graph transformation which preserves the nullity. As an application we determine the unbalanced bicyclic signed graphs of order n with nullity n-3 or n-4, and signed bicyclic signed graphs (including simple bicyclic graphs) of order n with nullity n-5.
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