ELA, Volume 9, pp. 158-170, August 2002, abstract.

On Spectra of Expansion Graphs and 
Matrix Polynomials, II

Karl-Heinz Forster and Bela Nagy


An expansion graph of a directed weighted graph 
G_0 is obtained from G_0 by replacing some edges 
by disjoint chains. The adjacency matrix of an 
expansion graph is a partial linearization of a 
matrix polynomial with nonnegative coefficients. 
The spectral radii for different expansion graphs 
of G_0 and correspondingly the spectral radii of
matrix polynomials with nonnegative coefficients, 
which sum up to a fixed matrix, are compared. 
A limiting formula is proved for the sequence of 
the spectral radii of a sequence of expansion graphs 
of G_0 when the lengths of all chains replacing
some original edges tend to infinity. It is shown 
that for all expansion graphs of G_0 the adjacency 
matrices have the same level characteristic, but 
they can have different height characteristics 
as examples show.