{"paper":{"title":"Secure Domination in Bisplit graphs -- A Structural and algorithmic study","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"N Sadagopan, Swathi D","submitted_at":"2025-12-30T05:11:18Z","abstract_excerpt":"A dominating set $S$ of a graph $G(V,E)$ is called a \\textit{secure dominating set} if each vertex $u \\in V(G) \\setminus S$ is adjacent to a vertex $v \\in S$ such that $(S \\setminus \\{v\\}) \\cup \\{u\\}$ is a dominating set of $G$. The \\textit{secure domination number} $\\gamma_s(G)$ of $G$ is the minimum cardinality of a secure dominating set of $G$. The \\textit{Minimum Secure Domination problem} is to find a secure dominating set of a graph $G$ of cardinality $\\gamma_s(G)$. In this paper, the computational complexity of the secure domination problem on several graph classes is investigated. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.23989","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.23989/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}