Resistance distance in bent linear 2-trees

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

Resistance distance in bent linear 2-trees

Combinatorics 2017-12-19 v1

Authors: Wayne Barrett , Emily J. Evans , Amanda E. Francis

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 $V(G_n) = \{ 1, 2, \ldots, n\}$ 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 $E(H_n) = (E(G_n) \cup \{k,k+3\})\setminus(\{k+1,k+3\}$ to be a bent linear 2-tree with bend at vertex $k$ .

Keywords

trees graph theory

Cite

@article{arxiv.1712.05859,
  title  = {Resistance distance in bent linear 2-trees},
  author = {Wayne Barrett and Emily J. Evans and Amanda E. Francis},
  journal= {arXiv preprint arXiv:1712.05859},
  year   = {2017}
}

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