Combinatorial upper bounds for the smallest eigenvalue of a graph

Aryan Esmailpour, Sara Saeedi Madani, Dariush Kiani

Let $G$ be a graph, and let $\hat{I}»(G)$ denote the smallest eigenvalue of $G$. First, we provide an upper bound for $\hat{I}»(G)$ based on induced bipartite subgraphs of $G$. Consequently, w…