The tau constant and the discrete Laplacian matrix of a metrized graph
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In this paper, the authors express the tau constant of a metrized graph in terms of the discrete Laplacian matrix and its pseudo-inverse, and show that it can be expressed asAbstract:
We express the tau constant of a metrized graph in terms of the discrete Laplacian matrix and its pseudo-inverse.read more
Citations
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The walk distances in graphs
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Zhang's Conjecture and the Effective Bogomolov Conjecture over function fields
TL;DR: In this paper, the Effective Bogomolov Conjecture over a function field of characteristic 0 was shown to be true for curves of genus at most 4 and a few other special cases.
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The Tau Constant of a Metrized Graph and its Behavior under Graph Operations
TL;DR: The tau constant of a metrized graph has been studied in this paper, where it has been shown that it changes when edges of a graph are replaced by arbitrary graphs.
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The tau constant of a metrized graph and its behavior under graph operations
TL;DR: Baker and Rumely's lower bound conjecture on the tau constant is proved for several classes of metrized graphs.
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Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces
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References
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Generalized Inverse of Matrices and Its Applications
TL;DR: In this article, the generalized inverse of matrices and its applications are discussed and discussed in terms of generalized inverse of matrix and its application in the context of generalization of matrix matrices.
Journal ArticleDOI
Laplacian matrices of graphs: a survey
TL;DR: In this paper, the authors survey some of the many results known for Laplacian matrices, and present a survey of the most important results in the field of graph analysis.
Journal ArticleDOI
Generalized Inverse of Matrices and its Applications
TL;DR: The Generalized Inverse of Matrices and its Applications is studied in detail in the context of discrete-time optimization and its applications.
Book
Matrices ' Methods and Applications'
TL;DR: In this article, a basic algebra of matrices is defined, including unique solution of linear equations, determinant and inverse rank, non-unique solution of equations, and applications.