## Further results on the nullity of signed graphs.(English)Zbl 1406.05064

Summary: The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we apply the coefficient theorem on the characteristic polynomial of a signed graph and give two formulae on the nullity of signed graphs with cut-points. As applications of the above results, we investigate the nullity of the bicyclic signed graph $$\Gamma(\infty(p,q,l))$$, obtain the nullity set of unbalanced bicyclic signed graphs, and thus determine the nullity set of bicyclic signed graphs.

### MSC:

 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C22 Signed and weighted graphs
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