Multiplicity Lists for the Eigenvalues of Symmetric Matrices with a Given Graph
Charles R. Johnson, António Leal Duarte, Carlos M. Saiago · 2006
This chapter assumes basic terminology from graph theory in Chapter 28 ; a good general graph theory reference is [ CL96 ]. For standard terms or concepts from matrix analysis, see Part 1 : Basic Linear Algebra, particularly Chapter 4.3, and Chapter 8 ; a good general matrix reference is [ HJ85 ]. As we will be interested in properties of A that are permutation similarity invariant, primarily eigenvalues and their multiplicities, we will generally view a graph as unlabeled, except when referencing by labels is convenient.