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Integral circulant graphs of prime power order with maximal energy

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Title: Integral circulant graphs of prime power order with maximal energy
Authors: Sander, J.W.1 sander@imai.uni-hildesheim.de, Sander, T.2 t.sander@ostfalia.de
Source: Linear Algebra & its Applications. Dec2011, Vol. 435 Issue 12, p3212-3232. 21p.
Subjects: Cayley graphs, Integrals, Eigenvalues, Matrices (Mathematics), Mathematical optimization, Divisor theory, Set theory, Approximation theory
Abstract: Abstract: The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count and a set of divisors of in such a way that they have vertex set and edge set . Using tools from convex optimization, we analyze the maximal energy among all integral circulant graphs of prime power order and varying divisor sets . Our main result states that this maximal energy approximately lies between and twice this value. We construct suitable divisor sets for which the energy lies in this interval. We also characterize hyperenergetic integral circulant graphs of prime power order and exhibit an interesting topological property of their divisor sets. [Copyright &y& Elsevier]
Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Integral circulant graphs of prime power order with maximal energy
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  Data: <searchLink fieldCode="DE" term="%22Cayley+graphs%22">Cayley graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Integrals%22">Integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Divisor+theory%22">Divisor theory</searchLink><br /><searchLink fieldCode="DE" term="%22Set+theory%22">Set theory</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink>
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  Data: Abstract: The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count and a set of divisors of in such a way that they have vertex set and edge set . Using tools from convex optimization, we analyze the maximal energy among all integral circulant graphs of prime power order and varying divisor sets . Our main result states that this maximal energy approximately lies between and twice this value. We construct suitable divisor sets for which the energy lies in this interval. We also characterize hyperenergetic integral circulant graphs of prime power order and exhibit an interesting topological property of their divisor sets. [Copyright &y& Elsevier]
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  Group: Ab
  Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.laa.2011.05.039
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      – Code: eng
        Text: English
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        Type: general
      – SubjectFull: Integrals
        Type: general
      – SubjectFull: Eigenvalues
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      – SubjectFull: Matrices (Mathematics)
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      – SubjectFull: Mathematical optimization
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      – SubjectFull: Divisor theory
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      – SubjectFull: Set theory
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      – SubjectFull: Approximation theory
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      – TitleFull: Integral circulant graphs of prime power order with maximal energy
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              Text: Dec2011
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              Y: 2011
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