{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T17:52:35Z","timestamp":1764784355608,"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>The symmetric $m$-th power of a graph is the graph whose vertices are $m$-subsets of vertices and in which two $m$-subsets are adjacent if and only if their symmetric difference is an edge of the original graph. It was conjectured that there exists a fixed $m$ such that any two graphs are isomorphic if and only if their $m$-th symmetric powers are cospectral. In this paper we show that given a positive integer $m$ there exist infinitely many pairs of non-isomorphic graphs with cospectral $m$-th symmetric powers.  Our construction is based on theory of multidimensional extensions of coherent configurations.<\/jats:p>","DOI":"10.37236\/209","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:24:53Z","timestamp":1578716693000},"source":"Crossref","is-referenced-by-count":12,"title":["Non-Isomorphic Graphs with Cospectral Symmetric Powers"],"prefix":"10.37236","volume":"16","author":[{"given":"Amir Rahnamai","family":"Barghi","sequence":"first","affiliation":[]},{"given":"Ilya","family":"Ponomarenko","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,9,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r120\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r120\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:40:35Z","timestamp":1579315235000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r120"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/209","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,9,25]]},"article-number":"R120"}}