{"paper":{"title":"Domination Value in $P_2 \\square P_n$ and $P_2 \\square C_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eunjeong Yi","submitted_at":"2011-09-27T14:26:28Z","abstract_excerpt":"A set $D \\subseteq V(G)$ is a \\emph{dominating set} of a graph $G$ if every vertex of $G$ not in $D$ is adjacent to at least one vertex in $D$. A \\emph{minimum dominating set} of $G$, also called a $\\gamma(G)$-set, is a dominating set of $G$ of minimum cardinality. For each vertex $v \\in V(G)$, we define the \\emph{domination value} of $v$ to be the number of $\\gamma(G)$-sets to which $v$ belongs. In this paper, we find the total number of minimum dominating sets and characterize the domination values for $P_2 \\square P_n$ and $P_2 \\square C_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5908","kind":"arxiv","version":2},"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"}