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Monatshefte für Mathematik

, Volume 124, Issue 3, pp 215–235 | Cite as

The spectrum of the continuous Laplacian on a graph

  • Carla Cattaneo
Article

Abstract

We study the spectrum of the continuous Laplacian Δ on a countable connected locally finite graph Γ without self-loops, whose edges have suitable positive conductances and are identified with copies of segments [0, 1], with the condition that the sum of the weighted normal exterior derivatives is 0 at every node (Kirchhoff-type condition). In particular, we analyse the relation-between the spectrum of the operator Δ and the spectrum of the discrete Laplacian (I-P) defined on the vertices of Γ.

1991 Mathematics Subject Classification

47A10 

Key words

Spectrum continuous Laplacian discrete Laplacian, graph 

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Carla Cattaneo
    • 1
  1. 1.Dipartimento di MatematicaUniversità di MilanoMilanoItaly

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