Geodesic
Bounds for graph expansions via elasticity
The electronic journal of linear algebra, Tome 10 (2003), pp. 163-178.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In two recent papers, one by Friedland and Schneider, the other by F"orster 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.
Classification : 05C50, 15A48, 37B10, 92D25
Keywords: graph expansions, nonnegative matrices, elasticity, matrix polynomials 
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     author = {Neumann, Michael and Ormes, Nic},
     title = {Bounds for graph expansions via elasticity},
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Neumann, Michael; Ormes, Nic. Bounds for graph expansions via elasticity. The electronic journal of linear algebra, Tome 10 (2003), pp. 163-178. http://geodesic.mathdoc.fr/item/ELA_2003__10__a12/