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Journals / Hacettepe Journal of Mathematics and Statistics / 2013 / Cilt: 42 - Sayı: 5

AN UPPER BOUND ON THE SPECTRAL RADIUS OF WEIGHTED GRAPHS

S OZARSLAN
S SORGUN
S BUYUKKOSE
Pages
517–524
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

Wealso characterize graphs for which the bound is attained.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We consider weighted graphs, where the edge weights are positive definite matrices.
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Key Findings & Data:The eigenvalues of a graph are the eigenvalues of itsadjacency matrix.
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Conclusion & Impact:Wealso characterize graphs for which the bound is attained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Weighted graph · Adjacency matrix · Spectral radius

Abstract

We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of itsadjacency matrix. We obtain another upper bound which is sharp onthe spectral radius of the adjacency matrix and compare with someknown upper bounds with the help of some examples of graphs. Wealso characterize graphs for which the bound is attained.

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Cite This Article

OZARSLAN, S., SORGUN, S., BUYUKKOSE, S. (2022). AN UPPER BOUND ON THE SPECTRAL RADIUS OF WEIGHTED GRAPHS. Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 5, 517–524. https://ajindex.com/articles/530441

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