Algebraic Graph Theory-Shahla Nasserasr

Title: Multiplicities of Eigenvalues in Symmetric Graph Matrices with Zero Entries for Non-Edges

Abstract: This talk will focus on the multiplicities of eigenvalues in symmetric matrices associated with simple graphs, where nonzero entries correspond to edges, and zero entries represent non-edges in the off-diagonal positions. We will discuss how the structural properties of graphs, particularly those of trees, impact their spectral characteristics, with a special emphasis on eigenvalue multiplicities.