{"paper":{"title":"From the Coxeter graph to the Klein graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Italo J. Dejter","submitted_at":"2010-02-09T21:50:31Z","abstract_excerpt":"We show that the 56-vertex Klein cubic graph $\\G'$ can be obtained from the 28-vertex Coxeter cubic graph $\\G$ by 'zipping' adequately the squares of the 24 7-cycles of $\\G$ endowed with an orientation obtained by considering $\\G$ as a $\\mathcal C$-ultrahomogeneous digraph, where $\\mathcal C$ is the collection formed by both the oriented 7-cycles $\\vec{C}_7$ and the 2-arcs $\\vec{P}_3$ that tightly fasten those $\\vec{C}_7$ in $\\G$. In the process, it is seen that $\\G'$ is a ${\\mathcal C}'$-ultrahomogeneous (undirected) graph, where ${\\mathcal C}'$ is the collection formed by both the 7-cycles $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1960","kind":"arxiv","version":9},"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"}