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On Maximal Distance Energy

Author

Listed:
  • Shaowei Sun

    (School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China)

  • Kinkar Chandra Das

    (Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea)

  • Yilun Shang

    (Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK)

Abstract

Let G be a graph of order n . If the maximal connected subgraph of G has no cut vertex then it is called a block. If each block of graph G is a clique then G is called clique tree. The distance energy E D ( G ) of graph G is the sum of the absolute values of the eigenvalues of the distance matrix D ( G ) . In this paper, we study the properties on the eigencomponents corresponding to the distance spectral radius of some special class of clique trees. Using this result we characterize a graph which gives the maximum distance spectral radius among all clique trees of order n with k cliques. From this result, we confirm a conjecture on the maximum distance energy, which was given in Lin et al. Linear Algebra Appl 467(2015) 29-39.

Suggested Citation

  • Shaowei Sun & Kinkar Chandra Das & Yilun Shang, 2021. "On Maximal Distance Energy," Mathematics, MDPI, vol. 9(4), pages 1-7, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:360-:d:497508
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    References listed on IDEAS

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    1. Zhang, Minjie & Li, Shuchao, 2016. "Extremal cacti of given matching number with respect to the distance spectral radius," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 89-97.
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