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

Yong Lu, Jingwen Wu

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 t…