{"paper":{"title":"Grundy dominating sequences on $X$-join product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Graciela Nasini, Pablo Torres","submitted_at":"2018-10-05T15:05:34Z","abstract_excerpt":"In this paper we study the Grundy domination number on the $X$-join product $G\\hookleftarrow \\mathcal R$ of a graph $G$ and a family of graphs $\\mathcal R=\\{G_v: v\\in V(G)\\}$. The results led us to extend the few known families of graphs where this parameter can be efficiently computed. We prove that if, for all $v\\in V(G)$, the Grundy domination number of $G_v$ is given, and $G$ is a power of a cycle, a power of a path, or a split graph, computing the Grundy domination number of $G\\hookleftarrow \\mathcal R$ can be done in polynomial time. In particular, the results for power of cycles and pat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02737","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"}