部分立方体边超Wiener指数的计算方法及苯型体系的算法
A Method for Computing the Edge-Hyper-Wiener Index of Partial Cubes and an Algorithm for Benzenoid Systems
摘要：
连通图$G$的边超Wiener指标定义为$WW_e(G) = \frac{1}{2}\sum_{\lbrace e,f\rbrace \subseteq E(G)}d(e,f) + \frac{1}{2}\sum_{\lbrace e,f\rbrace \subseteq E(G)}d(e,f)^2$。部分立方体是一类有着广泛应用的图，本文提出了一种计算其边超Wiener指数的方法。它还显示了如何该方法可以应用到树。此外，得到了计算苯型体系的边超Wiener指数的算法。最后，该算法被用来纠正已知的闭公式的边Wiener指数和边超Wiener指数的线性多并苯。
英文摘要：
The edge-hyper-Wiener index of a connected graph $G$ is defined as $WW_e(G) = \frac{1}{2}\sum_{\lbrace e,f\rbrace \subseteq E(G)}d(e,f) + \frac{1}{2}\sum_{\lbrace e,f\rbrace \subseteq E(G)}d(e,f)^2$. We develop a method for computing the edge-hyper-Wiener index of partial cubes, which constitute a large class of graphs with a lot of applications. It is also shown how the method can be applied to trees. Furthermore, an algorithm for computing the edge-hyper-Wiener index of benzenoid systems is obtained. Finally, the algorithm is used to correct already known closed formulas for the edge-Wiener index and the edge-hyper-Wiener index of linear polyacenes.
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