{"paper":{"title":"$3$-Regular mixed graphs with optimum Hermitian energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xiaolin Chen, Xueliang Li, Yingying Zhang","submitted_at":"2014-12-11T14:57:56Z","abstract_excerpt":"Let $G$ be a simple undirected graph, and $G^\\phi$ be a mixed graph of $G$ with the generalized orientation $\\phi$ and Hermitian-adjacency matrix $H(G^\\phi)$. Then $G$ is called the underlying graph of $G^\\phi$. The Hermitian energy of the mixed graph $G^\\phi$, denoted by $\\mathcal{E}_H(G^\\phi)$, is defined as the sum of all the singular values of $H(G^\\phi)$. A $k$-regular mixed graph on $n$ vertices having Hermitian energy $n\\sqrt{k}$ is called a $k$-regular optimum Hermitian energy mixed graph. In this paper, we first focus on the problem proposed by Liu and Li [J. Liu, X. Li, Hermitian-adj"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3669","kind":"arxiv","version":2},"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"}