Comparison on the spectral radii of weighted digraphs that differ in a certain subdigraph

Abstract

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.

DOI: 10.1016/j.endm.2016.09.016

Cite this paper

@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} }