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On the sharp bounds of bicyclic graphs regarding edge Szeged index

Author

Listed:
  • Yao, Yan
  • Ji, Shengjin
  • Li, Guang

Abstract

For a given graph G, its edge Szeged index is denoted by Sze(G)=∑e=uv∈E(G)mu(e)mv(e), where mu(e) and mv(e) are the number of edges in G with distance to u less than to v and the number of edges in G further (distance) to u than v, respectively. In the paper, the bounds of edge Szeged index on bicyclic graphs are determined. Furthermore, the graphs that achieve the bounds are completely characterized.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:377:y:2020:i:c:s0096300320301041
    DOI: 10.1016/j.amc.2020.125135
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    References listed on IDEAS

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    1. 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.
    2. Wang, Guangfu & Li, Shuchao & Qi, Dongchao & Zhang, Huihui, 2018. "On the edge-Szeged index of unicyclic graphs with given diameter," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 94-106.
    3. 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.
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    1. Wang, Guangfu & Li, Shuchao & Qi, Dongchao & Zhang, Huihui, 2018. "On the edge-Szeged index of unicyclic graphs with given diameter," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 94-106.
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