## Submatrix monotonicity of the Perron root, II, Linear Algebra Appl

- S. Furtado, C. R. Johnson, C. Marijuán, M. Pisonero
- Electronic Notes in Discrete Mathematics
- 2014

1 Excerpt

- Published 2016 in Electronic Notes in Discrete Mathematics

Let DS be a weighted digraph of order n with a subdigraph S of order k, M(DS) its adjacency weight matrix and ρ(DS) its spectral radius. We consider the class Ck of weighted digraphs of order k and we study the preorder in Ck given by DS′ DS if and only if ρ(DS′) ≤ ρ(DS). We obtain that this order is equivalent to the entry-wise order M(DS′) ≤ M(DS). Several points of view are taken, under varying regularity conditions, and k polynomial conditions for the comparison are presented.

@article{Furtado2016ComparisonOT,
title={Comparison on the spectral radii of weighted digraphs that differ in a certain subdigraph},
author={S. Furtado and C. R. Johnson and C. Mariju{\'a}n and M. Pisonero},
journal={Electronic Notes in Discrete Mathematics},
year={2016},
volume={54},
pages={85-90}
}