Computation of Polarized Metrized Graph Invariants by Using Discrete Laplacian Matrix
No Thumbnail Available
Date
2015
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Amer Mathematical Soc
Open Access Color
BRONZE
Green Open Access
Yes
OpenAIRE Downloads
77
OpenAIRE Views
174
Publicly Funded
No
BIP! Indicators
Impulse
Average
Influence
Average
Popularity
Average
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.
Description
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, Resistance function, Mathematics - Number Theory, The discrete Laplacian matrix, Metrized graph, The tau constant, Polarized metrized graph, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO), Pseudo inverse and relative dualizing sheaf, Invariants of polarized metrized graphs, discrete Laplacian matrix, polarized metrized graph, Heights, Graph algorithms (graph-theoretic aspects), Applications of graph theory to circuits and networks, relative dualizing sheaf, tau constant, Arithmetic varieties and schemes; Arakelov theory; heights, metrized graph, Varieties over global fields, Distance in graphs, Graphs and linear algebra (matrices, eigenvalues, etc.), Programming involving graphs or networks, pseudo inverse, Curves of arbitrary genus or genus \(\ne 1\) over global fields, resistance function, invariants of polarized metrized graphs
Turkish CoHE Thesis Center URL
Fields of Science
0102 computer and information sciences, 01 natural sciences, 0101 mathematics
Citation
WoS Q
Q1
Scopus Q
Q2
OpenCitations Citation Count
2
Source
Mathematics of Computation
Volume
84
Issue
296
Start Page
2953
End Page
2967
PlumX Metrics
Citations
CrossRef : 2
Scopus : 3
Captures
Mendeley Readers : 2
SCOPUS™ Citations
3
checked on Feb 03, 2026
Web of Science™ Citations
3
checked on Feb 03, 2026
Page Views
5
checked on Feb 03, 2026
Google Scholar™
