{"paper":{"title":"Arithmetical structures on graphs with connectivity one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Carlos E. Valencia, Hugo Corrales","submitted_at":"2016-06-12T15:08:26Z","abstract_excerpt":"Given a graph $G$, an arithmetical structure on $G$ is a pair of positive integer vectors $({\\bf d},{\\bf r})$ such that $\\mathrm{gcd}({\\bf r}_v\\, | \\,v\\in V(G))=1$ and \\[ (\\mathrm{diag}({\\bf d})-A){\\bf r}=0, \\] where $A$ is the adjacency matrix of $G$. We describe the arithmetical structures on graph $G$ with a cut vertex $v$ in terms of the arithmetical structures on their blocks. More precisely, if $G_1,\\ldots,G_s$ are the induced subgraphs of $G$ obtained from each of the connected components of $G-v$ by adding the vertex $v$ and their incident edges, then the arithmetical structures on $G$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03726","kind":"arxiv","version":3},"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"}