Functional Analysis, Linear Structures and Applications Seminar  RSS

28/07/2017, 16:00 — 17:00 — Room 6.2.33, Faculty of Sciences of the Universidade de Lisboa
, Institute for Research in Fundamental Sciences, Tehran, Iran

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 $k$.

Current organizers: Helena Mascarenhas, Ângela Mestre.

CEAFEL FCT