Notes on the values of volume entropy of graphs

Wooyeon Kim; Seonhee Lim

doi:10.3934/dcds.2020221

Article Contents

2020, Volume 40, Issue 9: 5117-5129. Doi: 10.3934/dcds.2020221

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Notes on the values of volume entropy of graphs

Wooyeon Kim^1, and
Seonhee Lim^2, ,

1.
Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA
2.
Department of Mathematical Sciences, Seoul National University, Seoul, Republic of Korea

^* Corresponding author: Seonhee Lim
^* Corresponding author: Seonhee Lim

Received: September 2018

Revised: December 2019

Published: June 2020

This work was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1601-03 and the National Research Foundation of Korea(NRF) (NRF-2017R1E1A1A03070779, 2017R1A5A1015626)

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Abstract

Volume entropy is an important invariant of metric graphs as well as Riemannian manifolds. In this note, we calculate the change of volume entropy when an edge is added to a metric graph or when a vertex and edges around it are added. In the second part, we estimate the value of the volume entropy which can be used to suggest an algorithm for calculating the persistent volume entropy of graphs.

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Mathematics Subject Classification: 37D40, 37B40, 92Bxx.

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References

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