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Note on the Minimal Energy Ordering of Conjugated Trees

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Intelligent Computing Technology (ICIC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7389))

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Abstract

For a simple graph G, the energy E(G) is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix A(G). Gutman proposed two conjectures on the minimal energy of the class of conjugated trees (trees having a perfect matching). Zhang and Li determined the trees in the class with the minimal and second-minimal energies, which confirms the conjectures. Zhang and Li also found that the conjugated tree with the third-minimal energy is one of the two graphs which are quasi-order incomparable. Recently, Huo, Li and Shi found there exists a fixed positive integer N 0, such that for all n > N 0, the energy of the graphs with the third-minimal through the sixth-minimal are determined. In this paper, the N 0 is fixed by a recursive method, and the problem is solved completely.

Supported by NSFC and Youth Innovation foundation of Qinghai Normal University.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Qinghai Normal University, China

    Yulan Xiao & Bofeng Huo

  2. Ministry of Education and Qinghai Province, Key Lab of Tibetan Information Processing (Qinghai Normal University), Xining, 810008, P.R. China

    Bofeng Huo

Authors
  1. Yulan Xiao
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  2. Bofeng Huo
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Editor information

Editors and Affiliations

  1. School of Electronics and Information Engineering, Machine Learning and Systems Biology Laboratory, Tongji University, 4800 Caoan Road, 201804, Shanghai, China

    De-Shuang Huang

  2. School of Electronics and Information Engineering, Tongji University, 4800 Caoan Road, 201804, Shanghai, China

    Changjun Jiang

  3. Electrical and Electronics Department, Polytechnic of Bari, Via Orabona, 4, 70125, Bari, Italy

    Vitoantonio Bevilacqua

  4. Faculty of Engineering, District University Francisco José de Caldas, Cra. 7a No. 40-53, Fifth Floor, Bogotá, Colombia

    Juan Carlos Figueroa

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© 2012 Springer-Verlag Berlin Heidelberg

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Xiao, Y., Huo, B. (2012). Note on the Minimal Energy Ordering of Conjugated Trees. In: Huang, DS., Jiang, C., Bevilacqua, V., Figueroa, J.C. (eds) Intelligent Computing Technology. ICIC 2012. Lecture Notes in Computer Science, vol 7389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31588-6_27

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  • DOI: https://doi.org/10.1007/978-3-642-31588-6_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31587-9

  • Online ISBN: 978-3-642-31588-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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