{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T14:16:23Z","timestamp":1773584183489,"version":"3.50.1"},"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>Two graphs $G$ and $H$ are called $\\mathbb{R}$-cospectral if $A(G)+yJ$ and $A(H)+yJ$ (where $A(G)$, $A(H)$ are the adjacency matrices of $G$ and $H$, respectively, $J$ is the all-one matrix) have the same spectrum for all $y\\in\\mathbb{R}$. In this note, we give a necessary condition for having $\\mathbb{R}$-cospectral graphs. Further, we provide a sufficient condition ensuring only irrational orthogonal similarity between certain cospectral graphs. Some concrete examples are also supplied to exemplify the main results.<\/jats:p>","DOI":"10.37236\/6002","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T14:08:29Z","timestamp":1578665309000},"source":"Crossref","is-referenced-by-count":3,"title":["A Note on Non-$\\mathbb{R}$-Cospectral Graphs"],"prefix":"10.37236","volume":"24","author":[{"given":"Fenjin","family":"Liu","sequence":"first","affiliation":[]},{"given":"Wei","family":"Wang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,3,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p48\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T00:03:34Z","timestamp":1579219414000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i1p48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,17]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1,20]]}},"URL":"https:\/\/doi.org\/10.37236\/6002","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,17]]},"article-number":"P1.48"}}