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Maximizing and Minimizing Multiplicative Zagreb Indices of Graphs Subject to Given Number of Cut Edges

Author

Listed:
  • Shaohui Wang

    (Department of Mathematics, Savannah State University, Savannah, GA 31419, USA
    These authors contributed equally to this work.)

  • Chunxiang Wang

    (School of Mathematics and Statistics and Hubei key Laboratory Mathematics Sciences, Central China Normal University, Wuhan 430079, China
    These authors contributed equally to this work.)

  • Lin Chen

    (School of Mathematics and Statistics and Hubei key Laboratory Mathematics Sciences, Central China Normal University, Wuhan 430079, China
    These authors contributed equally to this work.)

  • Jia-Bao Liu

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
    These authors contributed equally to this work.)

  • Zehui Shao

    (Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
    These authors contributed equally to this work.)

Abstract

Given a (molecular) graph, the first multiplicative Zagreb index Π 1 is considered to be the product of squares of the degree of its vertices, while the second multiplicative Zagreb index Π 2 is expressed as the product of endvertex degree of each edge over all edges. We consider a set of graphs G n , k having n vertices and k cut edges, and explore the graphs subject to a number of cut edges. In addition, the maximum and minimum multiplicative Zagreb indices of graphs in G n , k are provided. We also provide these graphs with the largest and smallest Π 1 ( G ) and Π 2 ( G ) in G n , k .

Suggested Citation

  • Shaohui Wang & Chunxiang Wang & Lin Chen & Jia-Bao Liu & Zehui Shao, 2018. "Maximizing and Minimizing Multiplicative Zagreb Indices of Graphs Subject to Given Number of Cut Edges," Mathematics, MDPI, vol. 6(11), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:227-:d:179036
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    References listed on IDEAS

    as
    1. Borovićanin, Bojana & Furtula, Boris, 2016. "On extremal Zagreb indices of trees with given domination number," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 208-218.
    2. Gao, Wei & Farahani, Mohammad Reza & Wang, Shaohui & Husin, Mohamad Nazri, 2017. "On the edge-version atom-bond connectivity and geometric arithmetic indices of certain graph operations," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 11-17.
    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.
    4. Liu, Jia-Bao & Pan, Xiang-Feng & Hu, Fu-Tao & Hu, Feng-Feng, 2015. "Asymptotic Laplacian-energy-like invariant of lattices," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 205-214.
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