{"paper":{"title":"Domination in 4-regular Kn\\\"odel graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Doost Ali Mojdeh, Esmaeil Nazari, Seyed Reza Musawi","submitted_at":"2018-04-07T12:22:07Z","abstract_excerpt":"A subset $D$ of vertices of a graph $G$ is a dominating set if for each $u\\in V(G)\\setminus D$, $u$ is adjacent to some vertex $v\\in D$. The domination number, $\\gamma(G)$ of $G$, is the minimum cardinality of a dominating set of $G$. For an even integer $n\\ge2$ and $1\\le\\Delta\\le\\lfloor\\log_2n\\rfloor$, a Kn\\\"odel graph $W_{\\Delta,n}$ is a $Delta$-regular bipartite graph of even order $n$, with vertices$(i,j)$, for $i=1,2$ and $0\\le j\\le n/2-1$, where for every $j$, $0\\le j\\le n/2-1$, there is an edge between $(1,j)$ and $(2,j+2^k-1 \\text{(mod(n/2)})$, for $k=0,1,\\cdots,\\Delta-1$. In this pape"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02550","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"}