{"paper":{"title":"The domination number and the least $Q$-eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guanglong Yu, Rong Zhang, Shu-Guang Guo, Yarong Wu","submitted_at":"2013-10-17T14:31:57Z","abstract_excerpt":"A vertex set $D$ of a graph $G$ is said to be a dominating set if every vertex of $V(G)\\setminus D$ is adjacent to at least a vertex in $D$, and the domination number $\\gamma(G)$ ($\\gamma$, for short) is the minimum cardinality of all dominating sets of $G$. For a graph, the least $Q$-eigenvalue is the least eigenvalue of its signless Laplacian matrix. In this paper, for a nonbipartite graph with both order $n$ and domination number $\\gamma$, we show that $n\\geq 3\\gamma-1$, and show that it contains a unicyclic spanning subgraph with the same domination number $\\gamma$. By investigating the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4717","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"}