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ELASTIC GRAPHS

Part of: Variational problems in infinite-dimensional spaces Low-dimensional dynamical systems Graph theory

Published online by Cambridge University Press:  13 August 2019

DYLAN P. THURSTON Open the ORCID record for DYLAN P. THURSTON [Opens in a new window]
DYLAN P. THURSTON*
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA; [email protected]

Abstract

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An elastic graph is a graph with an elasticity associated to each edge. It may be viewed as a network made out of ideal rubber bands. If the rubber bands are stretched on a target space there is an elastic energy. We characterize when a homotopy class of maps from one elastic graph to another is loosening, that is, decreases this elastic energy for all possible targets. This fits into a more general framework of energies for maps between graphs.

MSC classification

Primary: 37E25: Maps of trees and graphs
Secondary: 58E20: Harmonic maps , etc. 05C21: Flows in graphs
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 7 , 2019 , e24
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author 2019

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