Finding a diagonal matrix congruent to A−cI for constants c, where A is the adjacency matrix of a graph G allows us to quickly tell the number of eigenvalues in a given interval. If G has clique-width k and a corresponding k-expression is known, then diagonalization can be done in time O(poly(k)n) where n is the order of G.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics