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Journals / Gazi University Journal of Science / 2026 / Volume: 28 Issue: 1

Improved Bounds for the Extremal Non-Trivial Laplacian Eigenvalues

Şerife Büyükköse
Ercan Altınışık
Feyza Yalçın
Pages
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Publication Date
2015-02-23
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this paper, we present an upper bound for the algebraic connectivity µn-1 of G and a lower bound for the largest eigenvalue µ1 of G in terms of the degree sequence d1,d2,…,dn of G and the number Ni∩Nj of common vertices of i and j (1≤i<j≤n) and hence we improve bounds of Maden and Büyükköse [14].

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let G be a simple connected graph and its Laplacian eigenvalues be µ1≥ µ2≥…≥ µn-1≥ µn=0.
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Key Findings & Data:Let G be a simple connected graph and its Laplacian eigenvalues be µ1≥ µ2≥…≥ µn-1≥ µn=0.
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Conclusion & Impact:In this paper, we present an upper bound for the algebraic connectivity µn-1 of G and a lower bound for the largest eigenvalue µ1 of G in terms of the degree sequence d1,d2,…,dn of G and the number Ni∩Nj of common vertices of i and j (1≤i<j≤n) and hence we improve bounds of Maden and Büyükköse [14].
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Laplacian eigenvalues · upper bounds · lower bounds

Abstract

Let G be a simple connected graph and its Laplacian eigenvalues be µ1≥ µ2≥…≥ µn-1≥ µn=0. In this paper, we present an upper bound for the algebraic connectivity µn-1 of G and a lower bound for the largest eigenvalue µ1 of G in terms of the degree sequence d1,d2,…,dn of G and the number Ni∩Nj of common vertices of i and j (1≤i<j≤n) and hence we improve bounds of Maden and Büyükköse [14].

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Cite This Article

Büyükköse, Ş., Altınışık, E., Yalçın, F. (2015). Improved Bounds for the Extremal Non-Trivial Laplacian Eigenvalues. Gazi University Journal of Science, Volume: 28 Issue: 1. https://ajindex.com/articles/1269621

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