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On the Wiener polarity index of graphs

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  • Hua, Hongbo
  • Das, Kinkar Ch.

Abstract

The Wiener polarity index Wp(G) of a graph G is the number of unordered pairs of vertices {u, v} in G such that the distance between u and v is equal to 3. Very recently, Zhang and Hu studied the Wiener polarity index in [Y. Zhang, Y. Hu, 2016] [38]. In this short paper, we establish an upper bound on the Wiener polarity index in terms of Hosoya index and characterize the corresponding extremal graphs. Moreover, we obtain Nordhaus–Gaddum-type results for Wp(G). Our lower bound on Wp(G)+Wp(G¯) is always better than the previous lower bound given by Zhang and Hu.

Suggested Citation

  • Hua, Hongbo & Das, Kinkar Ch., 2016. "On the Wiener polarity index of graphs," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 162-167.
    • Handle: RePEc:eee:apmaco:v:280:y:2016:i:c:p:162-167
    DOI: 10.1016/j.amc.2016.01.043
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    References listed on IDEAS

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    1. Das, Kinkar Ch. & Gutman, Ivan & Nadjafi–Arani, Mohammad J., 2015. "Relations between distance–based and degree–based topological indices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 142-147.
    2. Li, Jing & Li, Yiyang, 2015. "The asymptotic value of the zeroth-order Randić index and sum-connectivity index for trees," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1027-1030.
    3. Zhang, Yanhong & Hu, Yumei, 2016. "The Nordhaus–Gaddum-type inequality for the Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 880-884.
    4. 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.
    5. Shi, Yongtang, 2015. "Note on two generalizations of the Randić index," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1019-1025.
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    Cited by:

    1. Lei, Hui & Li, Tao & Ma, Yuede & Wang, Hua, 2018. "Analyzing lattice networks through substructures," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 297-314.
    2. Ashrafi, Ali Reza & Ghalavand, Ali, 2017. "Ordering chemical trees by Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 301-312.
    3. Noureen, Sadia & Bhatti, Akhlaq Ahmad & Ali, Akbar, 2021. "Towards the solution of an extremal problem concerning the Wiener polarity index of alkanes," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Ali, Akbar & Du, Zhibin & Ali, Muhammad, 2018. "A note on chemical trees with minimum Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 231-236.

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