  The eccentricity matrix of a connected graph $G$ is obtained from the
distance matrix of $G$ by retaining the largest distances in each row and each
column, and setting the remaining entries as $0$. In this article, a conjecture
about the least eigenvalue of eccentricity matrices of trees, presented in the
article [Jianfeng Wang, Mei Lu, Francesco Belardo, Milan Randic. The
anti-adjacency matrix of a graph: Eccentricity matrix. Discrete Applied
Mathematics, 251: 299-309, 2018.], is solved affirmatively. In addition to
this, the spectra and the inertia of eccentricity matrices of various classes
of graphs are investigated.
