# CEAFEL Seminar

On Friday, 28/07/2017, 16:00 — 17:00, in Room 6.2.33, Faculty of Sciences of the Universidade de Lisboa will take place a seminar by
Ali Mohammadian , Institute for Research in Fundamental Sciences, Tehran (Iran), with title

Integral Graphs

A graph $G$ is called integral if all eigenvalues of its adjacency matrix, $A(G)$, consist entirely of integers. The nullity of $G$ is the nullity of $A(G)$, that is the multiplicity of $0$ as an eigenvalue of $A(G)$. In this talk, we are concerned with integral trees. These objects are extremely rare and very difficult to find. We first present a short survey on integral graphs. We show that for any integer $d \gt 1$, there are infinitely many integral trees of diameter $d$. We will also show that for any integer $k \gt 1$, there are only finitely many integral trees with nullity $k$.