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Using Laplacian Eigenvalues and Eigenvectors in the Analysis of Frequency Assignment Problems

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  • Jan van den Heuvel
  • Snežana Pejić

Abstract

A Frequency Assignment Problem (FAP) is the problem that arises when frequencies have to be assigned to a given set of transmitters so that spectrum is used efficiently and the interference between the transmitters is minimal. In this paper we see the frequency assignment problem as a generalised graph colouring problem, where transmitters are presented by vertices and interaction between two transmitters by a weighted edge. We generalise some properties of Laplacian matrices that hold for simple graphs. We investigate the use of Laplacian eigenvalues and eigenvectors as tools in the analysis of properties of a FAP and its generalised chromatic number (the so-called span). Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Jan van den Heuvel & Snežana Pejić, 2001. "Using Laplacian Eigenvalues and Eigenvectors in the Analysis of Frequency Assignment Problems," Annals of Operations Research, Springer, vol. 107(1), pages 349-368, October.
    • Handle: RePEc:spr:annopr:v:107:y:2001:i:1:p:349-368:10.1023/a:1014927805247
    DOI: 10.1023/A:1014927805247
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