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.


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