ELA, Volume 10, pp. 163-178, July 2003, abstract.
Bounds for Graph Expansions via Elasticity
M. Neumann and N. Ormes
In two recent papers, one by Friedland and Schneider,
the other by Forster and Nagy, the authors used
polynomial matrices to study the effect of graph
expansions on the spectral radius of the adjacency
matrix. Here it is shown that the notion of the
elasticity of the entries of a nonnegative matrix
coupled with the Variational Principle for Pressure
from symbolic dynamics can be used to derive sharper
bounds than existing estimates. This is achieved for
weighted and unweighted graphs, and the case of equality
is characterized. The work is within the framework of
studying measured graphs where each edge is assigned
a positive length as well as a weight.