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Solutions to unsolved problems on the minimal energies of two classes of trees

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  • Bai, Yongqiang
  • Ma, Hongping

Abstract

The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. Let Tn,p,Tn,d be the set of all trees of order n with p pendent vertices, diameter d, respectively. In this paper, we completely characterize the trees with second-minimal and third-minimal energy in Tn,p (Tn,d, respectively) for 4≤p≤n−9 (10≤d≤n−3, respectively), which solves the problems left in Ma (2014).

Suggested Citation

  • Bai, Yongqiang & Ma, Hongping, 2016. "Solutions to unsolved problems on the minimal energies of two classes of trees," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 49-56.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:49-56
    DOI: 10.1016/j.amc.2016.04.006
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    References listed on IDEAS

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    1. Renqian, Suonan & Ge, Yunpeng & Huo, Bofeng & Ji, Shengjin & Diao, Qiangqiang, 2015. "On the tree with diameter 4 and maximal energy," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 364-374.
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