Title: Distinct Eignvalues and Sensitivity
| Speaker: | Shahla Nasserasr |
| Affiliation: | Rochester Institute of Technology |
| Zoom: | Contact Soffia Arnadottir |
Abstract:
For a graph $G$, the class of real-valued symmetric matrices whose zero-nonzero pattern of off-diagonal entries is described by the adjacencies in $G$ is denoted by $S(G)$. The inverse eigenvalue problem for the multiplicities of the eigenvalues of $G$ is to determine for which ordered list of positive integers $m_1\geq m_2\geq \cdots\geq m_k$ with $\sum_{i=1}^{k} m_i=|V(G)|$, there exists a matrix in $S(G)$ with distinct eigenvalues ${\lambda_1,\lambda_2,\cdots, \lambda_k}$ such that $\lambda_i$ has multiplicity $m_i$. A related parameter is $q(G)$, the minimum number of distinct eigenvalues of a matrix in $S(G)$. The main focus of this talk will be on the parameter $q(G)$. A relationship between some of the techniques that are used in studying graphs with $q(G)=2$ and in solving the sensitivity conjecture will be presented. This is joint work with the Discrete Mathematics Research Group of Regina.