IMPROVED BOUNDS FOR THE SPECTRAL RADIUS OF DIGRAPHS

Year 2010, Volume: 39 Issue: 3, 313 - 318, 01.03.2010

Ş. Burcu Bozkurt A. Dilek Güngör

Abstract

IMPROVED BOUNDS FOR THE SPECTRAL RADIUS OF DIGRAPHS

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).

Keywords

Digraph, Spectral radius, Bound

References

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