{"paper":{"title":"Chromatic Zagreb indices for graphical embodiment of colour clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Johan Kok, Muhammad Kamran Jamil, Naduvath Sudev","submitted_at":"2016-11-01T02:22:44Z","abstract_excerpt":"For a colour cluster $\\mathbb{C} =(\\mathcal{C}_1,\\mathcal{C}_2, \\mathcal{C}_3,\\ldots,\\mathcal{C}_\\ell)$, where $\\mathcal{C}_i$ is a colour class such that $|\\mathcal{C}_i|=r_i$, a positive integer, we investigate two types of simple connected graph structures $G^{\\mathbb{C}}_1$, $G^{\\mathbb{C}}_2$ which represent graphical embodiments of the colour cluster such that the chromatic numbers $\\chi(G^{\\mathbb{C}}_1)=\\chi(G^{\\mathbb{C}}_2)=\\ell$ and $\\min\\{\\varepsilon(G^{\\mathbb{C}}_1)\\}=\\min\\{\\varepsilon(G^{\\mathbb{C}}_2)\\} =\\sum\\limits_{i=1}^{\\ell}r_i-1$. Therefore, the problem is the edge-minimal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01416","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"}