# PIMS-UVic Discrete Math Seminar: Shahla Nasserasr

## Topic

The number of distinct eigenvalues realized by a symmetric matrix with a given graph

## Details

For a simple graph $G$ on $n$ vertices, let $\mathcal{S}(G)$ be the set of all $n\times n$ real symmetric matrices $A=[a_{i,j}]$ with $a_{i,j}\neq 0$ if and only if $\{i,j\}$ is an edge of $G$. There are no restrictions on the diagonal entries of $A$. The inverse eigenvalue problem for a graph $G$ (IEP-G) seeks to determine all possible spectra of matrices in $\mathcal{S}(G)$.

One of the relaxations of the IEP-G is to determine the minimum number of distinct eigenvalues of a matrix in $\mathcal{S}(G)$ for a given graph $G$. This parameter is denoted by $q(G)$ and it is called the minimum number of distinct eigenvalues of $G$.

In this presentation, we will review some of the results and the techniques from recent developments about $q(G)$.

**Scientific, Seminar**

**September 28, 2023**

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