{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T20:53:15Z","timestamp":1765486395192,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>An oriented graph $G^{\\sigma}$ is a simple undirected graph $G$ with an orientation $\\sigma$, which assigns to each edge a direction so that $G^{\\sigma}$ becomes a directed graph. $G$ is called the underlying graph of $G^{\\sigma}$, and we denote by $Sp(G)$ the adjacency spectrum of $G$. Skew-adjacency matrix $S( G^{\\sigma} )$ of $G^{\\sigma}$ is introduced, and its spectrum $Sp_S( G^{\\sigma} )$ is called the skew-spectrum of $G^{\\sigma}$. The relationship between $Sp_S( G^{\\sigma} )$ and $Sp(G)$ is studied.  In particular, we prove that (i) $Sp_S( G^{\\sigma} ) = {\\bf i} Sp(G)$ for some orientation $\\sigma$ if and only if $G$ is bipartite, (ii) $Sp_S(G^{\\sigma}) = {\\bf i} Sp(G)$ for any orientation $\\sigma$ if and only if $G$ is a forest, where ${\\bf i}=\\sqrt{-1}$.<\/jats:p>","DOI":"10.37236\/270","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:23:50Z","timestamp":1578698630000},"source":"Crossref","is-referenced-by-count":44,"title":["Skew Spectra of Oriented Graphs"],"prefix":"10.37236","volume":"16","author":[{"given":"Bryan","family":"Shader","sequence":"first","affiliation":[]},{"given":"Wasin","family":"So","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,11,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n32\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T19:04:04Z","timestamp":1579287844000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1n32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/270","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,11,13]]},"article-number":"N32"}}