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

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, an...

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Bibliographic Details
Published inJournal of statistical physics Vol. 154; no. 4; pp. 1177 - 1190
Main Author Chair, Noureddine
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.02.2014
Springer
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Simple random walk
Effective resistance
Kirchhoff index
Resistor electrical network
First and mean first passage time
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Summary: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.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-014-0916-z