{"paper":{"title":"Total Domination Value in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cong X. Kang","submitted_at":"2012-04-18T04:12:39Z","abstract_excerpt":"A set $D \\subseteq V(G)$ is a \\emph{total dominating set} of $G$ if for every vertex $v \\in V(G)$ there exists a vertex $u \\in D$ such that $u$ and $v$ are adjacent. A total dominating set of $G$ of minimum cardinality is called a $\\gamma_t(G)$-set. For each vertex $v \\in V(G)$, we define the \\emph{total domination value} of $v$, $TDV(v)$, to be the number of $\\gamma_t(G)$-sets to which $v$belongs. This definition gives rise to \\emph{a local study of total domination} in graphs. In this paper, we study some basic properties of the $TDV$ function; also, we derive explicit formulas for the $TDV$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3970","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"}