Further Results on the Nullity of Signed Graphs

Abstract EN

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 Γ∞p,q,l, obtain the nullity set of unbalanced bicyclic signed graphs, and thus determine the nullity set of bicyclic signed graphs.