{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T06:40:23Z","timestamp":1764571223973,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A mixed graph $D$ is obtained from a simple graph $G$, the underlying graph of $D$, by orienting some edges of $G$. A simple graph $G$ is said to be ODHS (all orientations of $G$ are determined by their $H$-spectra) if every two $H$-cospectral graphs in $\\mathcal{D}(G)$ are switching equivalent to each other, where $\\mathcal{D}(G)$ is the set of all mixed graphs with $G$ as their underlying graph. In this paper, we characterize all bicyclic ODHS graphs and construct infinitely many ODHS graphs whose cycle spaces are of dimension $k$. For a\u00a0 connected graph $G$ whose cycle space is of dimension $k$, we also obtain an achievable upper bound $2^{2k-1} + 2^{k-1}$ for the number of switching equivalence classes in $\\mathcal{D}(G)$, which naturally is an upper bound of the number of\u00a0 cospectral classes in $\\mathcal{D}(G)$. To achieve these, we propose a valid method to estimate the number of switching equivalence classes in $\\mathcal{D}(G)$ based on the strong cycle basis, a special cycle basis\u00a0 introduced in this paper.<\/jats:p>","DOI":"10.37236\/9640","type":"journal-article","created":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T09:40:52Z","timestamp":1600422052000},"source":"Crossref","is-referenced-by-count":0,"title":["On Graphs whose Orientations are Determined by their Hermitian Spectra"],"prefix":"10.37236","volume":"27","author":[{"given":"Yi","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo-Jun","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,9,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p55\/8174","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p55\/8174","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T09:40:53Z","timestamp":1600422053000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p55"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,18]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9640","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,9,18]]},"article-number":"P3.55"}}