Some classes of connected signed graphs with girth $g$ and negative inertia index $\lceil \frac{g}{2}\rceil +1$

BeiYan Liu, Fang Duan

Let $\Gamma$ be a signed graph. The number of negative eigenvalues of the adjacency matrix of $\Gamma$ is called the negative inertia index of $\Gamma$, which is denoted by $i_{-}(\Gamma )$. The length o…