Geometriae Dedicata

, Volume 74, Issue 1, pp 95–112

Eigenvalue Comparison Theorems of the Discrete Laplacians for a Graph

  • Hajime Urakawa

DOI: 10.1023/A:1005008324245

Cite this article as:
Urakawa, H. Geometriae Dedicata (1999) 74: 95. doi:10.1023/A:1005008324245


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.

first eigenvalue Laplacian infinite graph degree 

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Hajime Urakawa
    • 1
  1. 1.Mathematics LaboratoriesGraduate School of Information Sciences, Tohoku UniversitySendaiJapan

Personalised recommendations