The maximum multiplicity of an eigenvalue of symmetric matrices with a given graph

2016/01/12 by Keivan Hassani Monfared, Sudipta Mallik, Monfared, Keivan Hassani +1
Computer Science · Engineering · Mathematics · #05C50 #65F18 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1601.02760

openalex publication_date 2016/01/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For a graph G, M(G) denotes the maximum multiplicity occurring of an eigenvalue of a symmetric matrix whose zero-nonzero pattern is given by edges of G. We introduce two combinatorial graph parameters T^-(G) and T⁺(G) that give a lower and an upper bound for M(G) respectively, and we show that these bounds are sharp.

Related

• The maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph
• Minimum number of distinct eigenvalues of graphs
• The Graphs for which the Maximum Multiplicity of an Eigenvalue is Two
• Achievable multiplicity partitions in the inverse eigenvalue problem of a graph
• Linear combinations of graph eigenvalues