Resistance distance in regular graphs
Resistance distance in regular graphs
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DOI：
10.1002/(sici)1097-461x(1999)71:3
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发表时间：
1999
影响因子：
2.2
通讯作者：
I. Lukovits;S. Nikolic;N. Trinajstic
中科院分区：
文献类型：
--
作者：
I. Lukovits;S. Nikolic;N. Trinajstic
本文将阻力距离作为(分子)图的一种新的内在度量，特别是将所有顶点对之间的阻力距离之和R视为图的不变量。证明了R(GN)和R(KN)，其中GN表示包含N个顶点的连通图，KN表示包含N个顶点的完全图。给出了两类正则图(圈和完全图)的R的计算公式。文中还给出了四个柏拉图分子的R值。他们根据施莱格尔图的复杂性，将所考虑的柏拉图固体排序为二十面体、立方体、八面体和四面体。这一顺序与许多其他经常使用的描述符获得的顺序一致。©1999 John Wiley&Sons，Inc.Int J Quant Chem 71：217-225,1999
This report considers the resistance distance as a recently proposed new intrinsic metric on (molecular) graphs, and in particular, the sum R over resistance distances between all pairs of vertices is considered as a graph invariant. It has been proved that R(GN)>R(KN), where GN denotes a connected graph containing N vertices and KN denotes a complete graph containing N vertices. The formulas to obtain the R for two classes of regular graphs (cycles and complete graphs) are derived. Numerical values of R for four Platonic molecules are also given. They ordered the considered Platonic solids as the icosahedron, the cube, the octahedron, and the tetrahedron according to complexity of their Schlegel graphs. This order agrees with those obtained by many other, frequently used descriptors. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 217–225, 1999