{"paper":{"title":"On $k$-rainbow independent domination in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aleksandra Tepeh, Douglas F. Rall, Tadeja Kraner \\v{S}umenjak","submitted_at":"2017-09-26T12:22:17Z","abstract_excerpt":"In this paper, we define a new domination invariant on a graph $G$, which coincides with the ordinary independent domination number of the generalized prism $G \\Box K_k$, called the $k$-rainbow independent domination number and denoted by $\\gamma_{{\\rm ri}k}(G)$. Some bounds and exact values concerning this domination concept are determined. As a main result, we prove a Nordhaus-Gaddum-type theorem on the sum for $2$-rainbow independent domination number, and show if G is a graph of order $n \\geq 3$, then $5\\leq \\gamma_{{\\rm ri}2}(G)+\\gamma_{{\\rm ri}2}(\\overline{G})\\leq n+3$, with both bounds "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08966","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"}