{"paper":{"title":"Certain Chromatic Sums of Some Cycle Related Graph Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Johan Kok, K. P. Chithra, N. K. Sudev","submitted_at":"2016-06-01T13:01:58Z","abstract_excerpt":"Let $\\mathcal{C} = \\{c_1,c_2, c_3, \\ldots,c_k\\}$ be a certain type of proper $k$-colouring of a given graph $G$ and $\\theta(c_i)$ denote the number of times a particular colour $c_i$ is assigned to the vertices of $G$. Then, the colouring sum of a given graph $G$ with respect to the colouring $\\cC$, denoted by $\\omega_{\\cC}(G)$, is defined to be $\\omega(\\cC) = \\sum\\limits_{i=1}^{k}i\\,\\theta(c_i)$. The colouring sums such as $\\chi$-chromatic sum, $\\chi^+$-chromatic sum, $b$-chromatic sum, $b^+$-chromatic sum etc. are some of these types of colouring sums that have been studied recently. Motivat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00268","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"}