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The Bounds of Vertex Padmakar–Ivan Index on k -Trees

Author

Listed:
  • Shaohui Wang

    (Department of Mathematics and Physics, Texas A&M International University, Laredo, TX 78041, USA)

  • Zehui Shao

    (Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China)

  • Jia-Bao Liu

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Bing Wei

    (Department of Mathematics, The University of Mississippi, University, MS 38677, USA)

Abstract

The Padmakar–Ivan ( P I ) index is a distance-based topological index and a molecular structure descriptor, which is the sum of the number of vertices over all edges u v of a graph such that these vertices are not equidistant from u and v . In this paper, we explore the results of P I -indices from trees to recursively clustered trees, the k -trees. Exact sharp upper bounds of PI indices on k -trees are obtained by the recursive relationships, and the corresponding extremal graphs are given. In addition, we determine the P I -values on some classes of k -trees and compare them, and our results extend and enrich some known conclusions.

Suggested Citation

  • Shaohui Wang & Zehui Shao & Jia-Bao Liu & Bing Wei, 2019. "The Bounds of Vertex Padmakar–Ivan Index on k -Trees," Mathematics, MDPI, vol. 7(4), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:324-:d:218874
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    References listed on IDEAS

    as
    1. John Estes & Bing Wei, 2014. "Sharp bounds of the Zagreb indices of k-trees," Journal of Combinatorial Optimization, Springer, vol. 27(2), pages 271-291, February.
    2. Shao, Zehui & Wu, Pu & Gao, Yingying & Gutman, Ivan & Zhang, Xiujun, 2017. "On the maximum ABC index of graphs without pendent vertices," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 298-312.
    3. Wang, Shaohui & Wang, Chunxiang & Liu, Jia-Bao, 2018. "On extremal multiplicative Zagreb indices of trees with given domination number," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 338-350.
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    Cited by:

    1. Frank Werner, 2020. "Graph-Theoretic Problems and Their New Applications," Mathematics, MDPI, vol. 8(3), pages 1-4, March.

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