{"paper":{"title":"More on the skew-spectra of bipartite graphs and Cartesian products of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huishu Lian, Xiaolin Chen, Xueliang Li","submitted_at":"2013-05-15T10:13:44Z","abstract_excerpt":"Given a graph $G$, let $G^\\sigma$ be an oriented graph of $G$ with the orientation $\\sigma$ and skew-adjacency matrix $S(G^\\sigma)$. Then the spectrum of $S(G^\\sigma)$ is called the skew-spectrum of $G^\\sigma$, denoted by $Sp_S(G^\\sigma)$. It is known that a graph $G$ is bipartite if and only if there is an orientation $\\sigma$ of $G$ such that $Sp_S(G^\\sigma)=iSp(G)$. In [D. Cui, Y. Hou, On the skew spectra of Cartesian products of graphs, Electron. J. Combin. 20(2013), #P19], Cui and Hou conjectured that such orientation of a bipartite graph is unique under switching-equivalence. In this pap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3414","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"}