# No signed graph with the nullity $\eta(G,\sigma)=|V(G)|-2m(G)+2c(G)-1$

@article{Lu2020NoSG, title={No signed graph with the nullity \$\eta(G,\sigma)=|V(G)|-2m(G)+2c(G)-1\$}, author={Yong Lu and Jingwen Wu}, journal={arXiv: Combinatorics}, year={2020} }

Let $G^{\sigma}=(G,\sigma)$ be a signed graph and $A(G,\sigma)$ be its adjacency matrix. Denote by $m(G)$ the matching number of $G$. Let $\eta(G,\sigma)$ be the nullity of $(G,\sigma)$. He et al. [Bounds for the matching number and cyclomatic number of a signed graph in terms of rank, Linear Algebra Appl. 572 (2019), 273--291] proved that $$|V(G)|-2m(G)-c(G)\leq\eta(G,\sigma)\leq |V(G)|-2m(G)+2c(G),$$ where $c(G)$ is the dimension of cycle space of $G$. Signed graphs reaching the lower bound…

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