{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T20:52:55Z","timestamp":1765486375577,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A graph $G$ is said to have a parity-linked orientation $\\phi$ if every even cycle $C_{2k}$ in $G^{\\phi}$ is evenly (resp. oddly) oriented whenever $k$ is even (resp. odd). In this paper, this concept is used to provide an affirmative answer to the following conjecture of D. Cui and Y. Hou [D. Cui, Y. Hou, On the skew spectra of Cartesian products of graphs, Electronic J. Combin. 20(2):#P19, 2013]: Let $G=G(X,Y)$ be a bipartite graph. Call the $X\\rightarrow Y$ orientation of $G,$ the canonical orientation. Let $\\phi$ be any orientation of $G$ and let $Sp_S(G^{\\phi})$ and $Sp(G)$ denote respectively the skew spectrum of $G^{\\phi}$ and the spectrum of $G.$ Then $Sp_S(G^{\\phi}) = {\\bf{i}} Sp(G)$ if and only if $\\phi$ is switching-equivalent to the canonical orientation of $G.$ Using this result, we determine the switch for a special family of oriented hypercubes $Q_d^{\\phi},$ $d\\geq 1.$ Moreover, we give an orientation of the Cartesian product of a bipartite graph and a graph, and then determine the skew spectrum of the resulting oriented product graph, which generalizes a result of Cui and Hou. Further this can be used to construct new families of oriented graphs with maximum skew energy.<\/jats:p>","DOI":"10.37236\/3331","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:12:44Z","timestamp":1578705164000},"source":"Crossref","is-referenced-by-count":16,"title":["Skew Spectra of Oriented Bipartite Graphs"],"prefix":"10.37236","volume":"20","author":[{"given":"A.","family":"Anuradha","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"Balakrishnan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolin","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xueliang","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huishu","family":"Lian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wasin","family":"So","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2013,11,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p18\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:11:05Z","timestamp":1579259465000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i4p18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,15]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/3331","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,11,15]]},"article-number":"P18"}}