论文标题
比较Wiener，Szeged和修订的仙人掌图上的Szeged Index
Comparing Wiener, Szeged and revised Szeged index on cactus graphs
论文作者
论文摘要
我们表明，在仙人掌图上，szeged索引在上面是维也纳索引的两倍。对于经修订的szeged索引，如果进一步限制了图类别，情况就会反转。也就是说，如果仙人掌图的所有块都是循环，则其修订后的szeged索引在下面以其维纳索引的两倍。此外，我们表明这些边界是尖锐的，并检查了平等的情况。在此过程中，我们提供了修订后的Szeged索引作为顶点的总和，这证明非常有用，并且在其他情况下可能很有趣。
We show that on cactus graphs the Szeged index is bounded above by twice the Wiener index. For the revised Szeged index the situation is reversed if the graph class is further restricted. Namely, if all blocks of a cactus graph are cycles, then its revised Szeged index is bounded below by twice its Wiener index. Additionally, we show that these bounds are sharp and examine the cases of equality. Along the way, we provide a formulation of the revised Szeged index as a sum over vertices, which proves very helpful, and may be interesting in other contexts.
