English

Further results on the nullity of signed graphs

Combinatorics 2016-11-25 v1

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 Γ((p,q,l))\Gamma(\infty(p,q,l)), obtain the nullity set of unbalanced bicyclic signed graphs, and thus determine the nullity set of bicyclic signed graphs.

Keywords

Cite

@article{arxiv.1309.0174,
  title  = {Further results on the nullity of signed graphs},
  author = {Yu Liu and Lhua You},
  journal= {arXiv preprint arXiv:1309.0174},
  year   = {2016}
}

Comments

17 pages. arXiv admin note: text overlap with arXiv:1207.6765, arXiv:1107.0400 by other authors

R2 v1 2026-06-22T01:18:33.734Z