Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599447 | Linear Algebra and its Applications | 2014 | 26 Pages |
Abstract
We consider the problem of determining those undirected n-vertex graphs with a corresponding Hermitian matrix that admits only two distinct eigenvalues, with multiplicities k and n−kn−k. After giving some general algebraic characterizations of these dual multiplicity graphs, we then prove two major graph theoretic necessary conditions on such graphs. Construction techniques are then developed, and these lead to a characterization of dual multiplicity graphs for which the lesser multiplicity is two.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Zhao Chen, Matthew Grimm, Paul McMichael, Charles R. Johnson,