Locating the Eigenvalues for Graphs of Small Clique-Width

  • Martin Fürer
  • Carlos Hoppen
  • David P. Jacobs
  • Vilmar Trevisan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10807)

Abstract

It is shown that if G has clique-width k, and a corresponding tree decomposition is known, then a diagonal matrix congruent to \(A - cI\) for constants c, where A is the adjacency matrix of the graph G of order n, can be computed in time \(O(k^2 n)\). This allows to quickly tell the number of eigenvalues in a given interval.

Keywords

Eigenvalues Clique-width Congruent matrices Efficient algorithms Parameterized algorithms 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Martin Fürer
    • 1
  • Carlos Hoppen
    • 2
  • David P. Jacobs
    • 3
  • Vilmar Trevisan
    • 2
  1. 1.Department of Computer Science and EngineeringPennsylvania State UniversityState CollegeUSA
  2. 2.Instituto de MatemáticaUniversidade Federal do Rio Grande do SulAlegreBrazil
  3. 3.School of ComputingClemson UniversityClemsonUSA

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