Tohoku Mathematical Journal

Growth and the spectrum of the Laplacian of an infinite graph

Koji Fujiwara

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Tohoku Math. J. (2), Volume 48, Number 2 (1996), 293-302.

First available in Project Euclid: 3 May 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58G99
Secondary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)


Fujiwara, Koji. Growth and the spectrum of the Laplacian of an infinite graph. Tohoku Math. J. (2) 48 (1996), no. 2, 293--302. doi:10.2748/tmj/1178225382.

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  • [Bl] R. BROOKS, A relation between growth and the spectrum of the Laplacian, Math. Z. 178 (1981), 501-508.
  • [B2] R. BROOKS, The spectral geometry of -regular graphs, J. Analyse Math. 57 (1991), 120-151
  • [DK] J. DODZIUK AND L. KARP, Spectral and function theory for combinatorial Laplacians, in "Geometr of Random Motion" (R. Durrett and M. A. Pinsky eds.) Contemporary Mathematics 73, Amer. Math. Soc. 1988, 25-40.
  • [Fo] R. FORMAN, Determinants of Laplacians on graphs, Topology 32 (1993), 35-46
  • [Fl] K. FUJIWARA, Eigenvalues of Laplacians on a closed Riemannianmanifold and its nets, Proc. Amer Math. Soc. 123 (1995), No. 8, 2585-2594.
  • [F2] K. FUJIWARA, Laplacian on rapidly branching trees, to appear in Duke Math. J.
  • [K] M. KANAI, Analytic invariants, and rough isometries between non-compact Riemannian manifolds, Lecture Notes in Math. 1201, Springer-Verlag, New York, 1986, 122-137.
  • [OU] Y. OHNO AND H. URAKAWA, On the first eigenvalue of the combinatorial Laplacian for a graph, Interdisciplinary Information Sciences 1 (1994), 33^46.
  • [Su] T. SUNADA, Fundamental groups and Laplacians, Lecture Notes in Math. 1339, Springer-Verlag, Ne York, 1988, 248-277.