Note on the Minimal Energy Ordering of Conjugated Trees

  • Yulan Xiao
  • Bofeng Huo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7389)


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.


extremal graph minimal energy quasi-order incomparable conjugated tree 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yulan Xiao
    • 1
  • Bofeng Huo
    • 1
    • 2
  1. 1.Department of MathematicsQinghai Normal UniversityChina
  2. 2.Ministry of Education and Qinghai ProvinceKey Lab of Tibetan Information Processing (Qinghai Normal University)XiningP.R. China

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