{"paper":{"title":"The distance domination of generalized de Bruijn and Kautz digraphs","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erfang Shan, Xiao Min, Yanxia Dong","submitted_at":"2015-04-05T03:36:22Z","abstract_excerpt":"Let $G=(V,A)$ be a digraph and $k\\ge 1$ an integer. For $u,v\\in V$, we say that the vertex $u$ distance $k$-dominate\n  $v$ if the distance from $u$ to $v$ at most $k$. A set $D$ of vertices in $G$ is a distance $k$-dominating set if for each vertex of $V\\setminus D$ is distance $k$-dominated by some vertex of $D$. The {\\em distance $k$-domination number} of $G$, denoted by $\\gamma_{k}(G)$, is the minimum cardinality of a distance $k$-dominating set of $G$. Generalized de Bruijn digraphs $G_B(n,d)$ and generalized Kautz digraphs $G_K(n,d)$ are good candidates for interconnection networks. Tian "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01078","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"}