Laplacian eigenvalue distribution for unicyclic graphs

Sunyo Moon and Seungkook Park

Applied Mathematics and Computation, 2025, vol. 485, issue C

Abstract: Let G be a graph and let mG[0,1) denote the number of Laplacian eigenvalues of G in the interval [0,1). For a tree T with diameter d, Guo, Xue, and Liu proved that mT[0,1)≥(d+1)/3. In this paper, we provide a lower bound for mG[0,1) when G is a unicyclic graph, in terms of the diameter and girth of G. Moreover, for the lollipop graph, under certain conditions on its diameter and girth, we give a formula for the exact value of mG[0,1).

Keywords: Laplacian eigenvalues; Unicyclic graph; Diameter; Girth (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:485:y:2025:i:c:s0096300324004831

DOI: 10.1016/j.amc.2024.129022

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