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

Sumin Huang and Shuchao Li

Physica A: Statistical Mechanics and its Applications, 2020, vol. 558, issue C

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.

Keywords: Resistance distance; Kirchhoff index; Moore–Penrose inverse (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120305215

DOI: 10.1016/j.physa.2020.124999

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