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

Fingerprint

Graph in graph theory
Energy
Absolute value
Eigenvalue
Adjacency Matrix
Upper and Lower Bounds
Equality
Complement
Lower bound
Upper bound
Invariant
Family

Keywords

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

Cite this

Haemers, W. H. (2012). Seidel Switching and Graph Energy. (CentER Discussion Paper; Vol. 2012-023). Tilburg: Operations research.
Haemers, W.H. / Seidel Switching and Graph Energy. Tilburg : Operations research, 2012. (CentER Discussion Paper).
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language = "English",
volume = "2012-023",
series = "CentER Discussion Paper",
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Haemers, WH 2012 'Seidel Switching and Graph Energy' CentER Discussion Paper, vol. 2012-023, Operations research, Tilburg.

Seidel Switching and Graph Energy. / Haemers, W.H.

Tilburg : Operations research, 2012. (CentER Discussion Paper; Vol. 2012-023).

Research output: Working paperDiscussion paperOther research output

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T1 - Seidel Switching and Graph Energy

AU - Haemers, W.H.

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N2 - 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.

AB - 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.

KW - Seidel switching

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KW - graph energy.

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Haemers WH. Seidel Switching and Graph Energy. Tilburg: Operations research. 2012. (CentER Discussion Paper).