On the spectral radius of weighted digraphs
DOI:
https://doi.org/10.4067/S071609172012000300005Keywords:
Weighted digraph, spectral radius, upper bound, digrafo con peso, radio espectral, límites superiores.Abstract
We consider the weighted digraphs in which the arc weights are positive definite matrices. We obtain some upper bounds for the spectral radius of these digraphs and characterize the digraphs achieving the upper bounds. Some known upper bounds are then special cases of our results.References
[1] D. M. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs, Academic Press, New York, 1980 (second revised ed., Barth, eidelberg, 1995).
[2] D. M. Cvetkovic, M. Doob , I. Gutman and A. Torgasev, Recent Results in the Theory of Graph Spectra, NorthHolland, 1988.
[3] F. Buckley and F. Harary, Distance in Graphs, (AddisonWesley, Redwood, 1990).
[4] G. H. Xu and C.Q. Xu, Sharp bounds for the spectral radius of digraphs. Linear Algebra Appl. 430, pp. 1607—1612, (2009).
[5] H. Minc, Nonnegative Matrices, Academic Press, New York, (1988).
[6] K. Ch. Das and R. . Bapat, A sharp upper bound on the spectral radius of weighted graphs. Discrete Math. 308, pp. 3180—3186, (2008).On the spectral radius of weighted digraphs 259.
[7] K. Ch. Das, Extremal graph characterization from the bounds of the spectral radius of weighted graphs. Appl. Math. Comput. 217, pp. 7420—7426 (2011).
[8] K. Ch. Das and R.B. Bapat, A sharp upper bound on the largest Laplacian eigenvalue of weighted graphs. Linear Algebra Appl. 409, pp. 153—165 (2005).
[9] K. Ch. Das, Extremal graph characterization from the upper bound of the Laplacian spectral radius of weighted graphs, Linear Algebra Appl. 407, pp. 55—69 (2007).
[10] R. A. Horn and C.R. Johnson, Matrix Ananlysis, Cambridge University Press, New York, (1985).
[11] S. B. Bozkurt and A.D. Gungor, Improved bounds for the spectral radius of digraphs. Hacettepe J. Math. Stat. 39 (3), pp. 313—318, (2010).
[12] X. D. Zhang and J.S. Li, Spectral radius of nonnegative matrices and digraphs. Acta Math. Sin.18 (2), pp. 293—300, (2002).
[2] D. M. Cvetkovic, M. Doob , I. Gutman and A. Torgasev, Recent Results in the Theory of Graph Spectra, NorthHolland, 1988.
[3] F. Buckley and F. Harary, Distance in Graphs, (AddisonWesley, Redwood, 1990).
[4] G. H. Xu and C.Q. Xu, Sharp bounds for the spectral radius of digraphs. Linear Algebra Appl. 430, pp. 1607—1612, (2009).
[5] H. Minc, Nonnegative Matrices, Academic Press, New York, (1988).
[6] K. Ch. Das and R. . Bapat, A sharp upper bound on the spectral radius of weighted graphs. Discrete Math. 308, pp. 3180—3186, (2008).On the spectral radius of weighted digraphs 259.
[7] K. Ch. Das, Extremal graph characterization from the bounds of the spectral radius of weighted graphs. Appl. Math. Comput. 217, pp. 7420—7426 (2011).
[8] K. Ch. Das and R.B. Bapat, A sharp upper bound on the largest Laplacian eigenvalue of weighted graphs. Linear Algebra Appl. 409, pp. 153—165 (2005).
[9] K. Ch. Das, Extremal graph characterization from the upper bound of the Laplacian spectral radius of weighted graphs, Linear Algebra Appl. 407, pp. 55—69 (2007).
[10] R. A. Horn and C.R. Johnson, Matrix Ananlysis, Cambridge University Press, New York, (1985).
[11] S. B. Bozkurt and A.D. Gungor, Improved bounds for the spectral radius of digraphs. Hacettepe J. Math. Stat. 39 (3), pp. 313—318, (2010).
[12] X. D. Zhang and J.S. Li, Spectral radius of nonnegative matrices and digraphs. Acta Math. Sin.18 (2), pp. 293—300, (2002).
Published
20121028
How to Cite
[1]
S. Burcu and D. Bozkurt, “On the spectral radius of weighted digraphs”, Proyecciones (Antofagasta, On line), vol. 31, no. 3, pp. 247259, Oct. 2012.
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