一类苯环的Kirchhoff指标（英文）

如果用单位电阻来代替图G中的每条边得到一个电网络,而顶点i和j之间的电阻距离（Resistance distance）定义为此网络中节点i和j之间的等效电阻的阻值.图G的Kirchhoff指标定义为G中所有点对之间的电阻距离和.本文利用循环矩阵的理论得到了一类苯环R_n的Kirchhoff指标的计算公式,而且我们证明了R_n的Kirchhoff指标渐近等于R_n的Wiener指标的一半.

On the Kirchhoff Index of Cyclic Phenylenes

The resistance distance between vertices i and j of a connected graph G is computed as the effective resistance between vertices i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor.The Kirchhoff index of a graph G is defined as the sum of resistance distances between all pairs of vertices of G.In this paper,we use the theory of circulant matrices to obtain the formula for the Kirchhoff index of the cyclic phenylenes R_n. Furthermore,we show that the Krichhoff index of R_n is approximately to one half of its Wiener index.