On the limit points of the smallest eigenvalues of regular graphs

2011/05/27 by Hyonju Yu, Yu, Hyonju
Chemistry · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Synthesis and Properties of Aromatic Compounds #math.CO

paper · pdf · doi:10.48550/arxiv.1105.5490

18pages

arxiv created 2011/05/27 · openalex publication_date 2011/05/27 · arxiv updated 2011/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [-1-√2, -2) and also infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [α₁, -1-√2) where α₁ is the smallest root(≈ -2.4812) of the polynomial x³+2x²-2x-2. From these results, we determine the largest and second largest limit points of smallest eigenvalues of regular graphs less than -2. Moreover we determine the supremum of the smallest eigenvalue among all connected 3-regular graphs with smallest eigenvalue less than -2 and we give the unique graph with this supremum value as its smallest eigenvalue.

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