Integral Laplacian graphs with a unique double Laplacian eigenvalue, I

2022/06/02 by Abdul Hameed, Hameed, Abdul, Mikhail Tyaglov +1
Chemistry · Materials Science · Mathematics · #05C50 #05C76 (Primary) 15A1 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Magnetism in coordination complexes #Metal-Organic Frameworks: Synthesis and Applications

paper · pdf · doi:10.48550/arxiv.2206.00980

openalex publication_date 2022/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The set S_i,n=\0,1,2,…,n-1,n\∖\i\, 1\leqslant i\leqslant n is called Laplacian realizable if there exists an undirected simple graph whose Laplacian spectrum is S_i,n. The existence of such graphs was established by S. Fallat et al. in 2005. In this paper, we investigate graphs whose Laplacian spectra have the form S_\i,j\_n^m=\0,1,2,…,m-1,m,m,m+1,…,n-1,n\∖\i,j\, 0<i></i>

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