Calculus on Graphs

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The purpose of this paper is to develop a "calculus" on graphs that allows graph theory to have new connections to analysis. For example, our framework gives rise to many new partial differential equations on graphs, most notably a new (Laplacian based) wave equation; this wave equation gives rise to a partial improvement on the Chung-Faber-Manteuffel diameter/eigenvalue bound in graph theory, and the Chung-Grigoryan-Yau and (in a certain case) Bobkov-Ledoux distance/eigenvalue bounds in analysis. Our framework also allows most techniques for the non-linear p-Laplacian in analysis to be easily carried over to graph theory.
63 pages, LaTeX

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Discrete Mathematics, Combinatorics, G.2.2

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http://salesiana.dossiersoluciones.com/handle/123456789/32285

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cs/0408028
 http://arxiv.org/abs/cs/0408028

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arXiv