Dirichlet p-Laplacian eigenvalues and Cheeger constants on symmetric graphs

Bobo Hua; Lili Wang

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arXiv · 1812.09667

Dirichlet p-Laplacian eigenvalues and Cheeger constants on symmetric graphs

Bobo Hua·Lili Wang

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Abstract

In this paper, we study eigenvalues and eigenfunctions of $p$-Laplacians with Dirichlet boundary condition on graphs. We characterize the first eigenfunction (and the maximum eigenfunction for a bipartite graph) via the sign condition. By the uniqueness of the first eigenfunction of $p$-Laplacian, as $p\to 1,$ we identify the Cheeger constant of a symmetric graph with that of the quotient graph. By this approach, we calculate various Cheeger constants of spherically symmetric graphs.

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BibTeX RIS

Bobo Hua, Lili Wang. 2018-12-23. Dirichlet p-Laplacian eigenvalues and Cheeger constants on symmetric graphs. https://arxiv.org/abs/1812.09667

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