Eigenvalue Comparison Theorems of the Discrete Laplacians for a Graph |
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| Authors: | Hajime Urakawa |
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| Institution: | (1) Mathematics Laboratories, Graduate School of Information Sciences, Tohoku University, Katahira 2-1-1, Sendai, 980-8577, Japan |
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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. |
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| Keywords: | first eigenvalue Laplacian infinite graph degree |
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