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Computation of polarized metrized graph invariants by using discrete Laplacian matrix


Author: Zubeyir Cinkir
Journal: Math. Comp. 84 (2015), 2953-2967
MSC (2010): Primary 14G40, 90C35, 94C15; Secondary 11G50, 11G35, 11G30
DOI: https://doi.org/10.1090/mcom/2981
Published electronically: May 8, 2015
MathSciNet review: 3378856
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Abstract: Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry have been studied recently. In this paper, we give fast algorithms to compute these invariants by expressing them in terms of the discrete Laplacian matrix and its pseudo inverse. The algorithm we give can be used for both symbolic and numerical computations. We present various examples to illustrate the implementation of these algorithms.


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Additional Information

Zubeyir Cinkir
Affiliation: Department of Mathematics, Zirve University, 27260, Gaziantep, Turkey
Address at time of publication: Department of Industrial Engineering, Abdullah Gul University, 38080, Kayseri, Turkey
Email: zubeyir.cinkir@agu.edu.tr

DOI: https://doi.org/10.1090/mcom/2981
Keywords: Metrized graph, polarized metrized graph, invariants of polarized metrized graphs, the tau constant, resistance function, the discrete Laplacian matrix, pseudo inverse and relative dualizing sheaf
Received by editor(s): February 24, 2012
Received by editor(s) in revised form: April 4, 2014
Published electronically: May 8, 2015
Article copyright: © Copyright 2015 American Mathematical Society