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On the resistance distance and Kirchhoff index of a linear hexagonal (cylinder) chain

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  • Huang, Sumin
  • Li, Shuchao

Abstract

The resistance between two nodes in some resistor networks has been studied extensively by mathematicians and physicists. Let Ln be a linear hexagonal chain with n6-cycles. Then identifying the opposite lateral edges of Ln in an ordered way yields the linear hexagonal cylinder chain, written as Rn. We obtain explicit formulae for the resistance distance rLn(i,j) (resp. rRn(i,j)) between any two vertices i and j of Ln (resp. Rn). One may see that {Ln}n=1∞ and {Rn}n=1∞ are two nontrivial families with diameter going to ∞ for which all resistance distances have been explicitly calculated. We determine the maximum and the minimum resistance distances in Ln (resp. Rn). The monotonicity and some asymptotic properties of resistance distances in Ln and Rn are given. As well we give formulae for the Kirchhoff indices of Ln and Rn respectively.

Suggested Citation

  • Huang, Sumin & Li, Shuchao, 2020. "On the resistance distance and Kirchhoff index of a linear hexagonal (cylinder) chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    • Handle: RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120305215
    DOI: 10.1016/j.physa.2020.124999
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    References listed on IDEAS

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    1. Jiang, Zhuozhuo & Yan, Weigen, 2017. "Resistance between two nodes of a ring network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 21-26.
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