Nodal domain theorem for the graph p-Laplacian
نویسندگان
چکیده
In this work we consider the nonlinear graph p-Laplacian and the set of eigenvalues and associated eigenvectors of this operator defined by a variational principle. We prove a unifying nodal domain theorem for the graph p-Laplacian for any p ≥ 1. While for p > 1 the bounds on the number of weak and strong nodal domains are the same as for the linear graph Laplacian (p = 2), the behavior changes for p = 1. We show that the bounds are tight for p ≥ 1 by studying the eigenvectors of the graph p-Laplacian for two example graphs where the bounds on the nodal domains are attained.
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عنوان ژورنال:
- CoRR
دوره abs/1602.05567 شماره
صفحات -
تاریخ انتشار 2016