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On the spectral radius of (0,1)-matrices. (English) Zbl 0563.15012
Authors’ summary: We determine the maximum spectral radius for (0,1)- matrices with $k\sp 2$ and $k\sp 2+1$ 1’s, respectively, and for symmetric (0,1)-matrices with zero trace and $e=\left( \matrix k\\ 2\endmatrix \right)$ 1’s (graphs with e edges). In all cases, equality is characterized.
Reviewer: N.J.Pullman

##### MSC:
 15B36 Matrices of integers 05C50 Graphs and linear algebra 15A18 Eigenvalues, singular values, and eigenvectors
Full Text:
##### References:
 [1] Doob, M.; Cvetcovic, D.; Sachs, H.: Spectra of graphs. (1982) [2] Gantmacher, F. R.: The theory of matrices. 2 (1959) · Zbl 0085.01001 [3] Parlett, B. N.: Spectra of graphs. (1980) · Zbl 0431.65016 [4] Schwarz, B.: Rearrangements of square matrices with non-negative elements. Duke math. J., 45-62 (1964) · Zbl 0121.26401 [5] S. Friedland, The maximum eigenvalue of 0-1 matrices with prescribed number of 1’s, to appear. · Zbl 0578.15010