The Nullity of Bicyclic Signed Graphs
Combinatorics
2014-09-19 v1
Abstract
Let \Gamma be a signed graph and let A(\Gamma) be the adjacency matrix of \Gamma. The nullity of \Gamma is the multiplicity of eigenvalue zero in the spectrum of A(\Gamma). In this paper we characterize the signed graphs of order n with nullity n-2 or n-3, and introduce a graph transformation which preserves the nullity. As an application we determine the unbalanced bicyclic signed graphs of order n with nullity n-3 or n-4, and signed bicyclic signed graphs (including simple bicyclic graphs) of order n with nullity n-5.
Cite
@article{arxiv.1207.6765,
title = {The Nullity of Bicyclic Signed Graphs},
author = {Yi-Zheng Fan and Wen-Xue Du and Chun-Long Dong},
journal= {arXiv preprint arXiv:1207.6765},
year = {2014}
}