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.