The Nullity of Bicyclic Signed Graphs
Let Γbe a signed graph and let A(Γ) be the adjacency matrix of Γ. The nullity of Γis the multiplicity of eigenvalue zero in the spectrum of A(Γ). 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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