Seidel Switching and Graph Energy

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Abstract

Abstract: The energy of a graph Γ is the sum of the absolute values of the eigenvalues of the adjacency matrix of Γ. Seidel switching is an operation on the edge set of Γ. In some special cases Seidel switching does not change the spectrum, and therefore the energy. Here we investigate when Seidel switching changes the spectrum, but not the energy. We present an infinite family of examples with very large (possibly maximal) energy. The Seidel energy S(Γ) of Γ is defined to be the sum of the absolute values of the eigenvalues of the Seidel matrix of G. It follows that S(Γ) is invariant under Seidel switching and taking complements. We obtain upper and lower bounds for S(Γ), characterize equality for the upper bound, and formulate a conjecture for the lower bound.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages8
Volume2012-023
Publication statusPublished - 2012

Publication series

NameCentER Discussion Paper
Volume2012-023

Keywords

  • Seidel switching
  • Seidel matrix
  • graph spectra
  • graph energy.

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