{"paper":{"title":"Neighbor product distinguishing total colorings of corona of subcubic graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aijun Dong, Wenwen Zhang","submitted_at":"2020-11-20T15:34:50Z","abstract_excerpt":"A proper $[k]$-total coloring $c$ of a graph $G$ is a mapping $c$ from $V(G)\\bigcup E(G)$ to $[k]=\\{1,2,\\cdots,k\\}$ such that $c(x)\\neq c(y)$ for which $x$, $y\\in V(G)\\bigcup E(G)$ and $x$ is adjacent to or incident with $y$. Let $\\prod(v)$ denote the product of $c(v)$ and the colors on all the edges incident with $v$. For each edge $uv\\in E(G)$, if $\\prod(u)\\neq \\prod(v)$, then the coloring $c$ is called a neighbor product distinguishing total coloring of $G$. we use $\\chi\"_{\\prod}(G)$ to denote the minimal value of $k$ in such a coloring of $G$. In 2015, Li et al. conjectured that $\\Delta(G)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.10455","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.10455/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"}