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Sufficient Conditions for a Graph to Be ℓ -Connected, ℓ -Deficient, ℓ -Hamiltonian and ℓ − -Independent in Terms of the Forgotten Topological Index

Author

Listed:
  • Guifu Su

    (College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China)

  • Shuai Wang

    (College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China)

  • Junfeng Du

    (College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China)

  • Mingjing Gao

    (College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, 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

The forgotten topological index of a (molecule) graph is the sum of cubes of all its vertex degrees, which plays a significant role in measuring the branching of the carbon atom skeleton. It is meaningful and difficult to explore sufficient conditions for a given graph keeping certain properties in graph theory. In this paper, we mainly explore sufficient conditions in terms of the forgotten topological index for a graph to be ℓ -connected, ℓ -deficient, ℓ -Hamiltonian and ℓ − -independent, respectively. The conditions cannot be dropped.

Suggested Citation

  • Guifu Su & Shuai Wang & Junfeng Du & Mingjing Gao & Kinkar Chandra Das & Yilun Shang, 2022. "Sufficient Conditions for a Graph to Be ℓ -Connected, ℓ -Deficient, ℓ -Hamiltonian and ℓ − -Independent in Terms of the Forgotten Topological Index," Mathematics, MDPI, vol. 10(11), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1802-:d:823557
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    References listed on IDEAS

    as
    1. Yilun Shang, 2015. "On the Hamiltonicity of random bipartite graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(2), pages 163-173, April.
    2. Guifu Su & Liming Xiong & Xiaofeng Su & Guojun Li, 2016. "Maximally edge-connected graphs and Zeroth-order general Randić index for $$\alpha \le -1$$ α ≤ - 1," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 182-195, January.
    3. Zhen-Mu Hong & Zheng-Jiang Xia & Fuyuan Chen & Lutz Volkmann & M. Irfan Uddin, 2021. "Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected," Complexity, Hindawi, vol. 2021, pages 1-11, February.
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