Unbounded resistance conjecture for linear 2-trees of growing diameter

Let $G$ be a linear 2-tree, and let its diameter tend to infinity. Let the maximal resistance distance of $G$ mean the maximum of $r_G(u,v)$ over pairs of vertices. Unbounded resistance conjecture. If the diameter of the linear 2-tree tends to infinity, then its maximal resistance distance is unbounded. The paper proves this for straight linear 2-trees and their connected subgraphs containing the two end vertices, while the assertion for arbitrary linear 2-trees is left as a conjecture.