A family of graphs that are determined by their normalized Laplacian spectra

2018/05/28 by Abraham Berman, Dongmei Chen, Berman, Abraham +7
Chemistry · Mathematics · Medicine · #05C50 #Alzheimer's disease research and treatments #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1805.10832

openalex publication_date 2018/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let F_p,q be the generalized friendship graph K₁\bigvee (pK_q) on pq+1 vertices obtained by joining a vertex to all vertices of p disjoint copies of the complete graph K_q on q vertices. In this paper, we prove that F_p,q is determined by its normalized Laplacian spectrum if and only if q≥ 2, or q=1 and p≤ 2.

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