[cs/0408028] Calculus on Graphs

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Computer Science > Discrete Mathematics

Title: Calculus on Graphs

Authors: Joel Friedman, Jean-Pierre Tillich

(Submitted on 12 Aug 2004)

Abstract: 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.

| ----- | | Comments: | 63 pages, LaTeX |
| Subjects: | Discrete Mathematics (cs.DM); Combinatorics (math.CO) |
| ACM classes: | G.2.2 |
| Cite as: | arXiv:cs/0408028 [cs.DM] |
| | (or arXiv:cs/0408028v1 [cs.DM] for this version) |