Effective resistances and Kirchhoff index in subdivision networks
Effective resistances and Kirchhoff index in subdivision networks
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DOI：
10.1080/03081087.2016.1256945
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发表时间：
2016-09
影响因子：
1.1
通讯作者：
Á. Carmona;M. Mitjana;Enric Monsó
中科院分区：
文献类型：
--
作者：
Á. Carmona;M. Mitjana;Enric Monsó
我们通过在给定网络的每条边插入一个新的顶点来定义一个细分网络，使得每条边被两条新边取代，这两条新边的电导满足新网络上的电条件。在这项工作中，我们首先根据基网络的Green核得到细分网络的Green核的表达式。此外，我们还根据基网络上相应的参数得到了细分网络的有效电阻和Kirchhoff指数。最后，以车轮为例进行了计算。
Abstract We define a subdivision network of a given network by inserting a new vertex in every edge, so that each edge is replaced by two new edges with conductances that fulfill electrical conditions on the new network. In this work, we firstly obtain an expression for the Green kernel of the subdivision network in terms of the Green kernel of the base network. Moreover, we also obtain the effective resistance and the Kirchhoff index of the subdivision network in terms of the corresponding parameters on the base network. Finally, as an example, we carry out the computations in the case of a wheel.