Article ID Journal Published Year Pages File Type
4599447 Linear Algebra and its Applications 2014 26 Pages PDF
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
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