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A lower bound of revised Szeged index of bicyclic graphs

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  • Ji, Shengjin
  • Liu, Mengmeng
  • Wu, Jianliang

Abstract

The revised Szeged index of a graph is defined as Sz*(G)=∑e=uv∈E(nu(e)+n0(e)2)(nv(e)+n0(e)2), where nu(e) and nv(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u, and n0(e) is the number of vertices equidistant to u and v. In the paper, we identify the lower bound of revised Szeged index among all bicyclic graphs, and also characterize the extremal graphs that attain the lower bound.

Suggested Citation

  • Ji, Shengjin & Liu, Mengmeng & Wu, Jianliang, 2018. "A lower bound of revised Szeged index of bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 480-487.
    • Handle: RePEc:eee:apmaco:v:316:y:2018:i:c:p:480-487
    DOI: 10.1016/j.amc.2017.08.051
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    References listed on IDEAS

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    1. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Digraphs with large maximum Wiener index," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 260-267.
    2. Bonamy, Marthe & Knor, Martin & Lužar, Borut & Pinlou, Alexandre & Škrekovski, Riste, 2017. "On the difference between the Szeged and the Wiener index," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 202-213.
    3. Lang, Rongling & Li, Tao & Mo, Desen & Shi, Yongtang, 2016. "A novel method for analyzing inverse problem of topological indices of graphs using competitive agglomeration," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 115-121.
    4. Lei, Hui & Yang, Hua, 2015. "Bounds for the Sum-Balaban index and (revised) Szeged index of regular graphs," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1259-1266.
    5. Črepnjak, Matevž & Tratnik, Niko, 2017. "The Szeged index and the Wiener index of partial cubes with applications to chemical graphs," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 324-333.
    6. Wang, Shujing, 2017. "On extremal cacti with respect to the Szeged index," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 85-92.
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    Cited by:

    1. Yao, Yan & Ji, Shengjin & Li, Guang, 2020. "On the sharp bounds of bicyclic graphs regarding edge Szeged index," Applied Mathematics and Computation, Elsevier, vol. 377(C).

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