The relationship between the negative inertia index of graph $G$ and its girth $g$ and diameter $d$

Songnian Xu, Wenhao Zhen, Dein Wong

Let $G$ be a simple connected graph. We use $n(G)$, $p(G)$, and $\eta (G)$ to denote the number of negative eigenvalues, positive eigenvalues, and zero eigenvalues of the adjacency mat…