Calculus on Graphs
<|reference_start|>Calculus on Graphs: 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.<|reference_end|>
@article{friedman2004calculus,
    title={Calculus on Graphs},
    author={Joel Friedman and Jean-Pierre Tillich},
    journal={arXiv preprint arXiv:cs/0408028},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0408028},
    primaryClass={cs.DM math.CO}
}