Note on the product of the largest and the smallest eigenvalue of a graph

2024/02/20 by Aida Abiad, Abiad, Aida, C. Dalfó +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2402.12915

openalex publication_date 2024/02/20 · openalex created_date 2024/06/04 · openalex updated_date 2026/07/28

Abstract

In this note, we use eigenvalue interlacing to derive an inequality between the maximum degree of a graph and its maximum and minimum adjacency eigenvalues. The case of equality is fully characterized.

Related

• Some observations on the smallest adjacency eigenvalue of a graph
• Eigenvalues and forbidden subgraphs I
• Graphs and Hermitian matrices: exact interlacing
• Combinatorial upper bounds for the smallest eigenvalue of a graph
• Improved lower bounds on the extrema of eigenvalues of graphs