{"paper":{"title":"Impact of Some Graph Operations on Double Roman Domination Number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anu V., Aparna Lakshmanan S.","submitted_at":"2019-08-19T14:58:38Z","abstract_excerpt":"Given a graph $G=(V,E)$, a function $f:V\\rightarrow \\{0,1,2,3\\}$ having the property that if $f(v)=0$, then there exist $ v_{1},v_{2}\\in N(v)$ such that $f(v_{1})=f(v_{2})=2$ or there exists $ w \\in N(v)$ such that $f(w)=3$, and if $f(v)=1$, then there exists $ w \\in N(v)$ such that $f(w)\\geq 2$ is called a double Roman dominating function (DRDF). The weight of a DRDF $f$ is the sum $f(V)=\\sum_{v\\in V}f(v)$. The double Roman domination number, $\\gamma_{dR}(G)$, is the minimum among the weights of DRDFs on $G$. In this paper, we study the impact of some graph operations, such as cartesian produ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06859","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06859/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"}