, Volume 74, Issue 1, pp 95-112

Eigenvalue Comparison Theorems of the Discrete Laplacians for a Graph

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Abstract

We give a graph theoretic analogue of Cheng's eigenvalue comparison theorems for the Laplacian of complete Riemannian manifolds. As its applications, we determine the infimum of the (essential) spectrum of the discrete Laplacian for infinite graphs.