On the difference between the Szeged index and the Wiener index of cacti
On the difference between the Szeged index and the Wiener index of cacti
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DOI：
10.1016/j.dam.2021.12.030
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发表时间：
2022-04
期刊：
影响因子：
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通讯作者：
Min Wang;Mengmeng Liu
中科院分区：
文献类型：
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作者：
Min Wang;Mengmeng Liu
仙人掌是一个连通图，其中任意两个环最多有一个公共顶点。设cn为所有周长至少为4的n顶点仙人掌的集合。Klavžar et al.（2018）证明了C n间图的seeged指数与Wiener指数之差的最小值和次最小值分别为2 n−5和4 n−10。在本文中，我们给出了一个反例来证明第二个结果是不成立的，并且我们确定了C n中图的seeged指数与Wiener指数之差的第二个最小值。
A cactus is a connected graph in which any two cycles have at most one common vertex. Let C n be the set of all n-vertex cacti with circumference at least 4. In Klavžar et al.(2018), the authors proved that the minimum and the second minimum values on the difference between the Szeged index and the Wiener index of graphs among C n are 2 n− 5 and 4 n− 10, respectively. In this paper, we give a counterexample to show that the second result is not true and we determine the second minimum value on the difference between the Szeged index and the Wiener index of graphs among C n.