Further results on the nullity of signed graphs
arXiv:1309.0174
Abstract
The nullity of a graph is the multiplicity of the eigenvalues zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we obtain the coefficient theorem of the characteristic polynomial of a signed graph, 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 , obtain the nullity set of unbalanced bicyclic signed graphs, and thus determine the nullity set of bicyclic signed graphs.
17 pages. arXiv admin note: text overlap with arXiv:1207.6765, arXiv:1107.0400 by other authors