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Dirichlet p-Laplacian eigenvalues and Cheeger constants on symmetric graphs

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 نشر من قبل Lili Wang
 تاريخ النشر 2018
  مجال البحث فيزياء
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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 $pto 1,$ 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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