Can one divide a graph into several connected parts with “good” properties? Possible mathematical formulations for this general question will be discussed in this chapter. In particular, we will see how the signs and the zeros of the eigenfunctions of graph matrices can be used for these purposes.

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Partitions and Eigenfunctions

  • Kiyan Naderi,
  • Konstantin Pankrashkin

摘要

Can one divide a graph into several connected parts with “good” properties? Possible mathematical formulations for this general question will be discussed in this chapter. In particular, we will see how the signs and the zeros of the eigenfunctions of graph matrices can be used for these purposes.