Seidel switching and graph energy

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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.
Original language English 653-659 MATCH, Communications in Mathematical and in Computer Chemistry 68 3 Published - 2012

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Graph in graph theory
Energy
Absolute value
Eigenvalue
Upper and Lower Bounds
Equality
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Cite this

title = "Seidel switching and graph energy",
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.",
author = "W.H. Haemers",
note = "Appeared earlier as CentER Discussion Paper 2012-023",
year = "2012",
language = "English",
volume = "68",
pages = "653--659",
journal = "MATCH, Communications in Mathematical and in Computer Chemistry",
issn = "0340-6253",
publisher = "University of Kragujevac, Faculty of Science",
number = "3",

}

In: MATCH, Communications in Mathematical and in Computer Chemistry, Vol. 68, No. 3, 2012, p. 653-659.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Seidel switching and graph energy

AU - Haemers, W.H.

N1 - Appeared earlier as CentER Discussion Paper 2012-023

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

M3 - Article

VL - 68

SP - 653

EP - 659

JO - MATCH, Communications in Mathematical and in Computer Chemistry

JF - MATCH, Communications in Mathematical and in Computer Chemistry

SN - 0340-6253

IS - 3

ER -