{"paper":{"title":"Unstable Graphs: A Fresh Outlook via TF-Automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Josef Lauri, Raffaele Scapellato, Russell Mizzi","submitted_at":"2014-01-25T15:52:24Z","abstract_excerpt":"In this paper, we first establish the very close link between stability of graphs, a concept first introduced in \\cite{Scapsalvi1} and studied most notably by Surowski \\cite{Surowski1}, \\cite{Surowski2} and Wilson \\cite{Wilson01} and two-fold automorphisms. The concept of two-fold isomorphisms, as far as we know, first appeared in literature in the form of isotopies of digraphs \\cite{zelinka4}, \\cite{zelinka1}, \\cite{zelinka2}, \\cite{zelinka3} and later studied formally in \\cite{lms1}, \\cite{lms2} with a greater emphasis on undirected graphs. We then turn our attention to the stability of grap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6552","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"}