Characterizing graphs with the second largest distance eigenvalue less than -1/2

Miriam Abdón, Lilian Markenzon, Cybele T. M. Vinagre

Let $G$ be a connected graph with vertex set $V$. The distance, $d_G(u,v)$, between vertices $u$ and $v$ of $G$ is defined as the length of a shortest path between $u$ and $v$ in…