scholarly journals Infinite reduction of divisors on metric graphs

2014 ◽  
Vol 35 ◽  
pp. 67-74 ◽  
Author(s):  
Spencer Backman
Keyword(s):  
Metric Graphs

scholarly journals On the nonlinear Dirac equation on noncompact metric graphs

2021 ◽  
Vol 278 ◽  
pp. 326-357
Author(s):  
William Borrelli ◽  
Raffaele Carlone ◽  
Lorenzo Tentarelli
Keyword(s):  
Dirac Equation ◽  
Metric Graphs ◽  
Nonlinear Dirac Equation

scholarly journals Heat kernels on metric graphs and a trace formula

2007 ◽  
pp. 175-198 ◽  
Author(s):  
Vadim Kostrykin ◽  
Jürgen Potthoff ◽  
Robert Schrader
Keyword(s):  
Trace Formula ◽  
Heat Kernels ◽  
Metric Graphs

Approximation Algorithms for the Star k-Hub Center Problem in Metric Graphs

2016 ◽  
pp. 222-234 ◽  
Author(s):  
Li-Hsuan Chen ◽  
Dun-Wei Cheng ◽  
Sun-Yuan Hsieh ◽  
Ling-Ju Hung ◽  
Chia-Wei Lee ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Center Problem ◽  
Metric Graphs

scholarly journals EMBEDDING OF METRIC GRAPHS ON HYPERBOLIC SURFACES

2019 ◽  
Vol 99 (03) ◽  
pp. 508-520
Author(s):  
BIDYUT SANKI
Keyword(s):  
Euler Characteristic ◽  
Isometric Embedding ◽  
Hyperbolic Surface ◽  
Hyperbolic Surfaces ◽  
Metric Graphs ◽  
Metric Graph ◽  
Complementary Region

An embedding of a metric graph $(G,d)$ on a closed hyperbolic surface is essential if each complementary region has a negative Euler characteristic. We show, by construction, that given any metric graph, its metric can be rescaled so that it admits an essential and isometric embedding on a closed hyperbolic surface. The essential genus $g_{e}(G)$ of $(G,d)$ is the lowest genus of a surface on which such an embedding is possible. We establish a formula to compute $g_{e}(G)$ and show that, for every integer $g\geq g_{e}(G)$ , there is an embedding of $(G,d)$ (possibly after a rescaling of $d$ ) on a surface of genus $g$ . Next, we study minimal embeddings where each complementary region has Euler characteristic $-1$ . The maximum essential genus $g_{e}^{\max }(G)$ of $(G,d)$ is the largest genus of a surface on which the graph is minimally embedded. We describe a method for an essential embedding of $(G,d)$ , where $g_{e}(G)$ and $g_{e}^{\max }(G)$ are realised.

scholarly journals Convergence of metric graphs and energy forms

2010 ◽  
pp. 367-448 ◽  
Author(s):  
Atsushi Kasue
Keyword(s):  
Metric Graphs
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