A Bound on the Diameter of a Graph Using the Number of Distinct Eigenvalues

Explore a fundamental theorem in spectral graph theory through this 31-minute lecture that establishes the relationship between a graph's diameter and the eigenvalues of its adjacency matrix. Learn how to prove that the diameter of any graph is strictly less than the number of distinct eigenvalues of its adjacency matrix, gaining insight into this important bound that connects geometric properties of graphs with their algebraic characteristics. Discover the mathematical techniques used to establish this inequality and understand its implications for graph analysis and network theory.