### 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 Γ. 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.

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 Γ. 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 language | English |
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Pages (from-to) | 653-659 |

Journal | MATCH, Communications in Mathematical and in Computer Chemistry |

Volume | 68 |

Issue number | 3 |

Publication status | Published - 2012 |

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### Cite this

Haemers, W. H. (2012). Seidel switching and graph energy.

*MATCH, Communications in Mathematical and in Computer Chemistry*,*68*(3), 653-659.