{"paper":{"title":"Resistance distance in bent linear 2-trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amanda E. Francis, Emily J. Evans, Wayne Barrett","submitted_at":"2017-12-15T22:11:45Z","abstract_excerpt":"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 $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05859","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}