{"paper":{"title":"Resistance distance in straight 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":"2017-12-16T00:46:23Z","abstract_excerpt":"We consider 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 $0<|i-j| \\leq 2$. We call $G_n$ the straight linear 2-tree on $n$ vertices. Using $\\Delta$--Y transformations and identities for the Fibonacci and Lucas numbers we obtain explicit formulae for the resistance distance $r_{G_n}(i,j)$ between any two vertices $i$ and $j$ of $G_n$. To our knowledge $\\{G_n\\}_{n=3}^\\infty$ is the first nontrivial family with diameter going to $\\infty$ for which all resistance distances have been explicitly calculated. Our result also gives formulae for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05883","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"}