Dirichlet p-Laplacian eigenvalues and Cheeger constants on symmetric graphs

• DOI: 10.1016/j.aim.2020.106997
• Publication Date: 2020-01-30T22:15:54Z
• Authors: Bobo Hua; Lili Wang
• Keywords: Eigenfunction

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.<br/>32 pages<br/>