{"paper":{"title":"A characterization of domination weak bicritical graphs with large diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michitaka Furuya","submitted_at":"2016-08-06T20:55:14Z","abstract_excerpt":"The domination number of a graph $G$, denoted by $\\gamma (G)$, is the minimum cardinality of a dominating set of $G$. A vertex of a graph is called critical if its deletion decreases the domination number, and a graph is called critical if its all vertices are critical. A graph $G$ is called weak bicritical if for every non-critical vertex $x\\in V(G)$, $G-x$ is a critical graph with $\\gamma (G-x)=\\gamma (G)$. In this paper, we characterize the connected weak bicritical graphs $G$ whose diameter is exactly $2\\gamma (G)-2$. This is a generalization of some known results concerning the diameter o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02154","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"}