A signed graph is a graph whose edges are labelled by a signature. It serves as a simple model of discrete vector bundle. We will explain nodal domain theorems for arbitrary symmetric matrices by exploring the induced signed graph structure. Applications to spectral theory of graph p-Laplacians will be discussed. For example, we will show that there is no other eigenvalue between the largest and the second largest variational eigenvalues of the graph p-Laplacian (p>1) on bipartite graphs. This talk is based on a joint work with Chuanyuan Ge and Dong Zhang.
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Meeting ID：836 9727 7124