Resistance distance in bent linear 2-trees

Wayne Barrett; Emily J. Evans; Amanda E. Francis

paper

Resistance distance in bent linear 2-trees

arXiv:1712.05859

Abstract

In this note we consider the bent linear 2-tree and provide an explicit formula for the resistance distance $r_{G_{n}} (1, n)$ between the first and last vertices of the graph. We call the graph $G_{n}$ with vertex set $V (G_{n}) = {1, 2, \dots, n}$ and ${i, j} \in E (G_{n})$ if and only if $0 < ∣ i - j ∣ \leq 2$ a straight linear 2-tree. We define the graph $H_{n}$ with $V (H_{n}) = V (G_{n})$ and $E (H_{n}) = (E (G_{n}) \cup {k, k + 3}) ∖ ({k + 1, k + 3}$ to be a bent linear 2-tree with bend at vertex $k$ .