{"paper":{"title":"Relation between the skew-rank of an oriented graph and the independence number of its underlying graph","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"H. Wang, J. Huang, S.C. Li","submitted_at":"2017-04-23T00:59:49Z","abstract_excerpt":"An oriented graph $G^\\sigma$ is a digraph without loops or multiple arcs whose underlying graph is $G$. Let $S\\left(G^\\sigma\\right)$ be the skew-adjacency matrix of $G^\\sigma$ and $\\alpha(G)$ be the independence number of $G$. The rank of $S(G^\\sigma)$ is called the skew-rank of $G^\\sigma$, denoted by $sr(G^\\sigma)$. Wong et al. [European J. Combin. 54 (2016) 76-86] studied the relationship between the skew-rank of an oriented graph and the rank of its underlying graph. In this paper, the correlation involving the skew-rank, the independence number, and some other parameters are considered. Fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06867","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"}