On the Spectral Radius of (0,1)-Matrices with 1’s in Prescribed Positions
Richard A. Brualdi, Suk-Geun Hwang · SIAM Journal on Matrix Analysis and Applications · 1996
Let n and d be positive integers with $1 \leq d \leq n ( n - 1 )/2$. We investigate the maximum and minimum spectral radii of a (0, 1)-matrix of order n that has 1’s on and below its main diagonal and d additional 1’s. If $d \leq 4$ we determine all matrices of this type that have the maximum spectral radius. For general d we prove an asymptotic result that severely limits the structure of matrices with maximum spectral radius. For $d \leq n$, we determine the minimum spectral radius.