Two-point resistances and random walks on stellated regular graphs
Two-point resistances and random walks on stellated regular graphs
复制标题
星状正则图上的两点阻力和随机游走
DOI：
10.1088/1751-8121/aaf8e7
复制
发表时间：
2019-02-15
影响因子：
2.1
通讯作者：
Klein, Douglas J.
中科院分区：
文献类型：
--
作者：
Yang, Yujun;Klein, Douglas J.
得到了正则图的星状图中任意两个顶点之间的电阻的计算公式。证明了星状图的两点电阻可以用原图的两点电阻来表示。结果，Kirchhoff指数（即所有对顶点之间的有效电阻之和）的星形图，这扩展了以前已知的结果。利用随机游动与电网络的对应关系，得到了星状图上随机游动的平均首达时间和平均通勤时间。
A formula for computing the resistance between any two vertices in the stellated graph of a regular graph is obtained. It turns out that the two-point resistance of the stellated graph can be expressed in terms of the two-point resistance of the original graph. As a consequence, the Kirchhoff index (i.e. the sum of the effective resistances between all pairs of vertices) for the stellated graph is obtained, which extends the previously known result. The correspondence between random walks and electric networks is then used to obtain the mean first passage time and mean commute time for random walks on stellated graphs.