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Journal of Applied Mathematics
Volume 2014, Article ID 483735, 8 pages
http://dx.doi.org/10.1155/2014/483735
Research Article

Further Results on the Nullity of Signed Graphs

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received 13 October 2013; Accepted 28 December 2013; Published 18 February 2014

Academic Editor: Qing-Wen Wang

Copyright © 2014 Yu Liu and Lihua You. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 , obtain the nullity set of unbalanced bicyclic signed graphs, and thus determine the nullity set of bicyclic signed graphs.