The nullity of bicyclic signed graphs.

Letbe a signed graph and letbe the adjacency matrix of. The nullity ofis the multiplicity of eigenvalue zero in the spectrum of. In this paper, we characterize the signed graphs of orderwith nullityor, and introduce a graph transformation which preserves the nullity. As an application we determine the unbalanced bicyclic signed graphs of orderwith nullityor, and signed bicyclic graphs (including simple bicyclic graphs) of orderwith nullity. [ABSTRACT FROM AUTHOR]