Submatrix monotonicity of the Perron root, II, Linear Algebra Appl
- S. Furtado, C. R. Johnson, C. Marijuán, M. Pisonero
- 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.