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Weighted graph Laplacians and isoperimetric inequalities

Weighted graph Laplacians and isoperimetric inequalities

We consider a weighted Cheeger's constant for a graph and we examine the gap between the first two eigenvalues of Laplacian.We establish several isoperimetric inequalities concerning the unweighted Cheeger's constant, weighted Cheeger's constants and eigenvalues for Neumann and Dirichlet conditions.