Advanced Discrete Mathematics & Math
Q86 / 100

What is algebraic graph theory's spectral theory?

Correct! Well done.

Incorrect.

The correct answer is B) Using eigenvalues of graph matrices (adjacency, Laplacian) to determine graph properties: connectivity, expansion, diameter, chromatic number bounds

B

Correct Answer

Using eigenvalues of graph matrices (adjacency, Laplacian) to determine graph properties: connectivity, expansion, diameter, chromatic number bounds

Explanation

Spectral graph theory: λ₁ (largest Laplacian eigenvalue) bounds chromatic number (χ ≤ λ₁+1). λ₂ (Fiedler value) measures connectivity/mixing. Expanders have large spectral gap. Used in clustering (spectral clustering, NCut).

Progress
86/100