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On extremal cacti with respect to the Szeged index

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  • Wang, Shujing

Abstract

The Szeged index of a graph G is defined as Sz(G)=∑e=uv∈Enu(e)nv(e), 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. A cactus is a graph in which any two cycles have at most one common vertex. Let C(n,k) denote the class of all cacti with order n and k cycles, and Cnt denote the class of all cacti with order n and t pendant vertices. In this paper, a lower bound of the Szeged index for cacti of order n with k cycles is determined, and all the graphs that achieve the lower bound are identified. As well, the unique graph in Cnt with minimum Szeged index is characterized.

Suggested Citation

  • Wang, Shujing, 2017. "On extremal cacti with respect to the Szeged index," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 85-92.
    • Handle: RePEc:eee:apmaco:v:309:y:2017:i:c:p:85-92
    DOI: 10.1016/j.amc.2017.03.036
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Hechao Liu & Hanyuan Deng & Zikai Tang, 2019. "Minimum Szeged index among unicyclic graphs with perfect matchings," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 443-455, August.
    2. 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.
    3. 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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