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On the edge-version atom-bond connectivity and geometric arithmetic indices of certain graph operations

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  • Gao, Wei
  • Farahani, Mohammad Reza
  • Wang, Shaohui
  • Husin, Mohamad Nazri

Abstract

Let dL(G)(e) be the degree of an edge e in line graph L(G) of a graph G. The edge versions of atom-bond connectivity (ABCe) and geometric arithmetic (GAe) indices of G are defined as ∑ef∈E(L(G))(dL(G)(e)+dL(G)(f)−2dL(G)(e)×dL(G)(f) and GAe(G)=∑ef∈E(L(G))2dL(G)(e)dL(G)(f)dL(G)(e)+dL(G)(f). In this paper, we study the ABCe and GAe indices for joint graphs and certain graph operations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:308:y:2017:i:c:p:11-17
    DOI: 10.1016/j.amc.2017.02.046
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    References listed on IDEAS

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    1. Gao, Wei & Wang, Weifan, 2016. "The eccentric connectivity polynomial of two classes of nanotubes," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 290-294.
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    Cited by:

    1. Raza, Hassan & Hayat, Sakander & Pan, Xiang-Feng, 2018. "On the fault-tolerant metric dimension of convex polytopes," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 172-185.
    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. Lin, Wenshui & Chen, Jianfeng & Wu, Zhixi & Dimitrov, Darko & Huang, Linshan, 2018. "Computer search for large trees with minimal ABC index," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 221-230.
    4. 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.

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