{"paper":{"title":"Measures of closeness to cordiality for graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amitabha Tripathi, Anand Brahmbhatt, Kartikeya Rai","submitted_at":"2024-11-07T06:05:54Z","abstract_excerpt":"A graph $G$ is cordial if there exists a function $f$ from the vertices of $G$ to $\\{0,1\\}$ such that the number of vertices labelled $0$ and the number of vertices labelled $1$ differ by at most $1$, and if we assign to each edge $xy$ the label $|f(x)-f(y)|$, the number of edges labelled $0$ and the number of edges labelled $1$ also differ at most by $1$. We introduce two measures of how close a graph is to being cordial, and compute these measures for a variety of classes of graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.04458","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.04458/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}