The graphs with all but two eigenvalues equal to -2 or 0

2016/01/21 by Sebastian M. Cioabă, Cioaba, Sebastian M., Willem H. Haemers +3
Computer Science · Mathematics · #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1601.05604

openalex publication_date 2016/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine all graphs for which the adjacency matrix has at most two eigenvalues (multiplicities included) not equal to -2, or 0, and determine which of these graphs are determined by their adjacency spectrum.

Related

• The graphs with all but two eigenvalues equal to ± 1
• The graphs with all but two eigenvalues equal to 2 or -1
• The signed graphs with two eigenvalues unequal to ± 1
• On signed graphs with at most two eigenvalues unequal to ± 1
• On graphs with exactly one anti-adjacency eigenvalue and beyond