{"paper":{"title":"Some Mixed Graphs Determined by Their Spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Ghafari, M.A. Nematollahi, M. Nahvi, S. Akbari","submitted_at":"2018-06-10T10:53:57Z","abstract_excerpt":"A mixed graph is obtained from a graph by orienting some of its edges. The Hermitian adjacency matrix of a mixed graph with the vertex set $ \\{v_{1}, \\ldots , v_{n}\\} $, is the matrix $ H=[h_{ij}]_{n \\times n} $, where $ h_{ij}=-h_{ji}=i $ if there is a directed edge from $ v_{i} $ to $ v_{j} $, $ h_{ij}=1 $ if there exists an undirected edge between $v_i$ and $v_{j}$, and $h_{ij}=0$ otherwise. The Hermitian spectrum of a mixed graph is defined to be the spectrum of its Hermitian adjacency matrix. In this paper we study mixed graphs which are determined by their Hermitian spectrum (DHS). First"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03634","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"}