{"paper":{"title":"Generalized power domination in WK-Pyramid Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Vijayakumar, Seethu Varghese","submitted_at":"2015-08-03T09:55:09Z","abstract_excerpt":"The notion of power domination arises in the context of monitoring an electric power system with as few phase measurement units as possible. The $k-$power domination number of a graph $G$ is the minimum cardinality of a $k-$power dominating set ($k-$PDS) of $G$. In this paper, we determine the $k-$power domination number of WK-Pyramid networks, $WKP_{(C,L)}$, for all positive values of $k$ except for $k=C-1, C \\geq 2$, for which we give an upper bound. The $k-$propagation radius of a graph $G$ is the minimum number of propagation steps needed to monitor the graph $G$ over all minimum $k-$PDS. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00357","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"}