Abstract
The maximum multiplicity among eigenvalues of matrices with a given graph cannot generally be expressed in terms of the degrees of the vertices (even when the graph is a tree). Given are best possible lower and upper bounds, and characterization of the cases of equality in these bounds. A by-product is a sequential algorithm to calculate the exact maximum multiplicity by simple counting.
Original language | English |
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Pages (from-to) | 27-31 |
Number of pages | 5 |
Journal | Electronic Journal Of Linear Algebra |
Volume | 9 |
Issue number | 3 |
DOIs | |
Publication status | Published - Mar 2002 |
Keywords
- Eigenvalues
- Multiplicity
- Symmetric matrix
- Tree
- Vertex degrees