Abstract
In this paper, we reveal the connection between the independent number of a graph and the topological multiplicity of the maximal eigenvalue of the corresponding graph 1-Laplacian. The pseudo independent number of a graph is introduced, which provides a better lower estimate of the topological multiplicity of the maximum eigenvalue. The technique of our proof is based on the localization property of the eigenvector for graph 1-Laplacian, the Krasnoselski genus, and its relation to the topological join.
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