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.