Open Access
58- https://doi.org/10.1080/01445340802354580
The graphs for which the maximum multiplicity of an eigenvalue is two
- Oct 1, 2009
- Linear and Multilinear Algebra
- Charles R Johnson +2 more
Abstract
Characterized are all simple undirected graphs G such that any real symmetric matrix that has graph G has no eigenvalues of multiplicity more than 2. All such graphs are partial 2-trees (and this follows from a result for rather general fields), but only certain partial 2-trees guarantee maximum multiplicity 2. Among partial linear 2-trees, they are only those whose vertices can be covered by two ‘parallel’ induced paths. The remaining graphs that guarantee maximum multiplicity 2 are composed of certain identified families of ‘exceptional’ partial 2-trees that are not linear.
- # Partial 2-trees
- # Simple Undirected Graphs
- # Eigenvalues Of Multiplicity
- # Real Symmetric Matrix
- # General Fields
- # Real Matrix
- # Simple Graphs
- # Undirected Graphs
