Resistance distance local rules
Resistance distance local rules
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DOI：
10.1007/s10910-007-9317-8
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发表时间：
2008-08
影响因子：
1.7
通讯作者：
Haiyan Chen;Fuji Zhang
中科院分区：
文献类型：
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作者：
Haiyan Chen;Fuji Zhang
在[D.J.克莱因，克罗地亚人。化学。 Acta.75(2), 633 (2002)]克莱因建立了许多求和规则来计算任意图的阻力距离，特别是他给出了一组特定的局部求和规则，确定了图的所有阻力距离（说局部求和规则集是完整的）。受这个结果的启发，我们给出了另一套完整的局部规则，它既简单又高效，特别是对于距离正则图。最后，一些化学图的应用（例如柏拉图固体及其顶点截断，其中包括巴克明斯特富勒烯的图和氮化硼异质富勒烯B12N12的图）来说明我们的方法。
In [D.J. Klein, Croat. Chem. Acta.75(2), 633 (2002)] Klein established a number of sum rules to compute the resistance distance of an arbitrary graph, especially he gave a specific set of local sum rules that determined all resistance distances of a graph (saying the set of local sum rules is complete). Inspired by this result, we give another complete set of local rules, which is simple and also efficient, especially for distance-regular graphs. Finally some applications to chemical graphs (for example the Platonic solids as well as their vertex truncations, which include the graph of Buckminsterfullerene and the graph of boron nitride hetero-fullerenoidB12N12) are made to illustrate our approach.