On the sum of the largest and smallest eigenvalues of odd-cycle free graphs

Aida Abiad, Vladislav Taranchuk, Thijs van Veluw

Let $G$ be a graph with adjacency eigenvalues ${\lambda }_1\ge \cdots \ge {\lambda }_n$. Both ${\lambda }_1+{\lambda }_n$ and the odd girth of $G$ can be seen as measures of the bipartiteness of $G$. Csikvári pr…