2021/03/08 by Rupert H. Levene, Levene, Rupert H., Polona Oblak +3
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory (math.SP) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2103.04587
openalex publication_date 2021/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that every 0-1 multiplicity matrix for a simple graph G is generically realisable for G. In particular, every multiplicity matrix for a path is generically realisable. We use this result to provide several families of joins of graphs that are realisable by a matrix with only two distinct eigenvalues.