### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 8 |

Volume | 2012-023 |

Publication status | Published - 2012 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2012-023 |

### Fingerprint

### Keywords

- Seidel switching
- Seidel matrix
- graph spectra
- graph energy.

### Cite this

*Seidel Switching and Graph Energy*. (CentER Discussion Paper; Vol. 2012-023). Tilburg: Operations research.

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

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Seidel Switching and Graph Energy

AU - Haemers, W.H.

N1 - Subsequently published in MATCH, Communications in Mathematical and in Computer Chemistry (2012) Pagination: 8

PY - 2012

Y1 - 2012

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

KW - Seidel matrix

KW - graph spectra

KW - graph energy.

M3 - Discussion paper

VL - 2012-023

T3 - CentER Discussion Paper

BT - Seidel Switching and Graph Energy

PB - Operations research

CY - Tilburg

ER -