2019/05/22 by Sumin Huang, Shuchao Li · 1 citation
Mathematics · #math.CO
paper · pdf · doi:10.1016/j.physa.2020.124999
20pages, 15 figures,
arxiv created 2019/05/22 · arxiv updated 2020/08/26
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 n 6-cycles. Then identifying the opposite lateral edges of Ln in 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). To the best of our knowledge \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.