{"paper":{"title":"Coloring Sums of Extensions of Certain Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Johan Kok, Saptarshi Bej","submitted_at":"2016-02-01T09:10:04Z","abstract_excerpt":"Recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted by $\\chi(G).$ In this paper the concepts of $\\chi$'-chromatic sum and $\\chi^+$-chromatic sum are introduced. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. We further the concepts of $\\chi$'-chromatic sum and $\\chi^+$-chromatic sum to extended paths and cycles. The paper concludes with \\emph{patterned structured} graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03735","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"}