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The Extremal Graphs of Some Topological Indices with Given Vertex k -Partiteness

Author

Listed:
  • Fang Gao

    (School of Mathematics and Computer Science, Chizhou University, Chizhou 247000, China)

  • Xiaoxin Li

    (School of Mathematics and Computer Science, Chizhou University, Chizhou 247000, China)

  • Kai Zhou

    (School of Mathematics and Computer Science, Chizhou University, Chizhou 247000, China)

  • Jia-Bao Liu

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

Abstract

The vertex k -partiteness of graph G is defined as the fewest number of vertices whose deletion from G yields a k -partite graph. In this paper, we characterize the extremal value of the reformulated first Zagreb index, the multiplicative-sum Zagreb index, the general Laplacian-energy-like invariant, the general zeroth-order Randi? index, and the modified-Wiener index among graphs of order n with vertex k -partiteness not more than m .

Suggested Citation

  • Fang Gao & Xiaoxin Li & Kai Zhou & Jia-Bao Liu, 2018. "The Extremal Graphs of Some Topological Indices with Given Vertex k -Partiteness," Mathematics, MDPI, vol. 6(11), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:271-:d:184371
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    References listed on IDEAS

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    1. Su, Guifu & Tu, Jianhua & Das, Kinkar Ch., 2015. "Graphs with fixed number of pendent vertices and minimal Zeroth-order general Randić index," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 705-710.
    2. Liu, Jia-Bao & Pan, Xiang-Feng, 2016. "Minimizing Kirchhoff index among graphs with a given vertex bipartiteness," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 84-88.
    3. Milovanović, E.I. & Milovanović, I.Ž. & Dolićanin, E.Ć. & Glogić, E., 2016. "A note on the first reformulated Zagreb index," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 16-20.
    4. 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.
    5. 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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