{"paper":{"title":"Total proper connection and graph operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xiaoyu Zhu, Yingying Zhang","submitted_at":"2017-05-06T14:19:27Z","abstract_excerpt":"A graph is said to be {\\it total-colored} if all the edges and vertices of the graph are colored. A path in a total-colored graph is a {\\it total proper path} if $(i)$ any two adjacent edges on the path differ in color, $(ii)$ any two internal adjacent vertices on the path differ in color, and $(iii)$ any internal vertex of the path differs in color from its incident edges on the path. A total-colored graph is called {\\it total-proper connected} if any two vertices of the graph are connected by a total proper path of the graph. For a connected graph $G$, the {\\it total proper connection number"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02487","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"}