The Effective Resistance of the $N$ -Cycle Graph with Four Nearest Neighbors

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• 作者：Noureddine Chair (1)
  
• 关键词：Effective resistance ; Kirchhoff index ; Resistor electrical network ; Simple random walk ; First and mean first passage time
• 刊名：Journal of Statistical Physics
• 出版年：2014
• 出版时间：February 2014
• 年：2014
• 卷：154
• 期：4
• 页码：1177-1190
• 全文大小：276 KB
• 作者单位：Noureddine Chair (1)
  
  1. Physics Department, The University of Jordan, Amman, Jordan
  
• ISSN：1572-9613

文摘

The exact expression for the effective resistance between any two vertices of the $N$ -cycle graph with four nearest neighbors $C_{N}(1,2)$ , is given. It turns out that this expression is written in terms of the effective resistance of the $N$ -cycle graph $C_{N}$ , the square of the Fibonacci numbers, and the bisected Fibonacci numbers. As a consequence closed form formulas for the total effective resistance, the first passage time, and the mean first passage time for the simple random walk on the the $N$ -cycle graph with four nearest neighbors are obtained. Finally, a closed form formula for the effective resistance of $C_{N}(1,2)$ with all first neighbors removed is obtained.