Achievable multiplicity partitions in the inverse eigenvalue problem of a graph

Abstract

Associated to a graph G is a set 𝒮(G) of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent, and the diagonal entries are free to be chosen. If G has n vertices, then the multiplicities of the eigenvalues of any matrix in 𝒮 (G) partition n; this is called a multiplicity partition.

Keywords

• inverse eigenvalue problem
• multiplicity partition
• adjacency matrix
• minimum rank
• distinct eigenvalues
• graphs
• 05c50
• 15a18