{"paper":{"title":"Relations between edge removing and edge subdivision concerning domination number of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Joaqu\\'in Tey, Magdalena Lema\\'nska, Rita Zuazua","submitted_at":"2014-09-26T09:16:44Z","abstract_excerpt":"Let $e$ be an edge of a connected simple graph $G$. The graph obtained by removing (subdividing) an edge $e$ from $G$ is denoted by $G-e$ ($G_e$). As usual, $\\gamma(G)$ denotes the domination number of $G$. We call $G$ an SR-graph if $\\gamma(G-e) = \\gamma(G_e)$ for any edge $e$ of $G$, and $G$ is an ASR-graph if $\\gamma(G - e) \\neq (G_e)$ for any edge $e$ of $G$. In this work we give several examples of SR and ASR-graphs. Also, we characterize SR-trees and show that ASR-graphs are $\\gamma$-insensitive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7508","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"}