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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 39 Issue: 3

IMPROVED BOUNDS FOR THE SPECTRAL RADIUS OF DIGRAPHS

Ş. Burcu Bozkurt
A. Dilek Güngör
Sayfa
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Yayın Tarihi
2010-03-01
DOI
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Xu and C.-Q Xu (Sharp bounds for the spectral radius of digraphs, Linear Algebra Appl. 430, 1607–1612, 2009).

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let G = (V, E) be a digraph with n vertices and m arcs without loops and multi-arcs.
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Temel Bulgular & Veri:The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix.
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Sonuç & Katkı:Xu and C.-Q Xu (Sharp bounds for the spectral radius of digraphs, Linear Algebra Appl. 430, 1607–1612, 2009).
🔬Tür:Research Article
📍Kapsam:2009 Verileri
⚙️Değişkenler:Digraph · Spectral radius · Bound

Abstract

Let G = (V, E) be a digraph with n vertices and m arcs without loops and multi-arcs. The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix. In this note, we obtain two sharp upper and lower bounds on ρ(G). These bounds improve those obtained by G. H. Xu and C.-Q Xu (Sharp bounds for the spectral radius of digraphs, Linear Algebra Appl. 430, 1607–1612, 2009).

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Bu Makaleye Atıf Yap

Bozkurt, Ş. B., Güngör, A. D. (2010). IMPROVED BOUNDS FOR THE SPECTRAL RADIUS OF DIGRAPHS. Hacettepe Journal of Mathematics and Statistics, Volume: 39 Issue: 3. https://ajindex.com/articles/1403697

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Kaynakça (6)

  1. Berman A. and Plemmons R. J. Nonnegative Matrices in Mathematics Sciences (Academic Press, New York, 1979).
  2. Cvetkovi´c D. M., Doob M., Gutman I. and Torgaˇsev, A. Recent Results in the Theory of Graph Spectra(North-Holland, 1988).
  3. Cvetkovi´c D. M., Doob M. and Sachs, H. Spectra of Graphs (Academic Press, New York, 1980). (Second revised ed., Barth, Heidelberg, 1995).
  4. Liu, H. and Lu, M. Sharp bounds on the spectral radius and the energy of graphs, MATCH Commun. Math. Comput. Chem. 59, 279–290, 2008.
  5. Xu, G.-H. and Xu, C.-Q. Sharp bounds for the spectral radius of digraphs, Linear Algebra Appl. 430, 1607–1612, 2009.
  6. Zhang, X.-D. and Li, J.-S. Spectral radius of nonnegative matrices and digraphs, Acta Math. Sin. 18 (2), 293–300, 2002.