{"paper":{"title":"A Linear Algorithm for Computing $\\gamma_{[1,2]}$-set in Generalized Series-Parallel Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"M.R. Hooshmandasl, P. Sharifani","submitted_at":"2017-07-20T11:02:48Z","abstract_excerpt":"For a graph $G=(V,E)$, a set $S \\subseteq V$ is a $[1,2]$-set if it is a dominating set for $G$ and each vertex $v \\in V \\setminus S$ is dominated by at most two vertices of $S$, i.e. $1 \\leq \\vert N(v) \\cap S \\vert \\leq 2$. Moreover a set $S \\subseteq V$ is a total $[1,2]$-set if for each vertex of $V$, it is the case that $1 \\leq \\vert N(v) \\cap S \\vert \\leq 2$. The $[1,2]$-domination number of $G$, denoted $\\gamma_{[1,2]}(G)$,is the minimum number of vertices in a $[1,2]$-set. Every $[1,2]$-set with cardinality of $\\gamma_{[1,2]}(G)$ is called a $\\gamma_{[1,2]}$-set. Total $[1,2]$-dominatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06443","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"}