Vertex-connectivity and $Q$-index of graphs with fixed girth

Huicai Jia, Hong-Jian Lai, Ruifang Liu +1

Let $q(G)$ denote the $Q$-index of a graph $G$, which is the largest signless Laplacian eigenvalue of $G$. We prove best possible upper bounds of $q(G)$ and best possible lower bou…