{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T16:19:43Z","timestamp":1778948383688,"version":"3.51.4"},"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>Let $\\mathcal{M}$ denote the Bose-Mesner algebra of a commutative $d$-class association scheme ${\\mathfrak X}$ (not necessarily symmetric), and $\\Gamma$ denote a (strongly) connected (directed) graph with adjacency matrix $A$. Under the assumption that $A$ belongs to $\\mathcal{M}$, we describe the combinatorial structure of $\\Gamma$. Moreover, we provide an algebraic-combinatorial characterization of $\\Gamma$ when $A$ generates $\\mathcal{M}$.\r\nAmong else, we show that, if ${\\mathfrak X}$ is a commutative $3$-class association scheme that is not an amorphic symmetric scheme, then we can always find a (directed) graph $\\Gamma$ such that the adjacency matrix $A$ of $\\Gamma$ generates the Bose-Mesner algebra $\\mathcal{M}$ of ${\\mathfrak X}$.<\/jats:p>","DOI":"10.37236\/12973","type":"journal-article","created":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T15:16:37Z","timestamp":1743088597000},"source":"Crossref","is-referenced-by-count":1,"title":["On Commutative Association Schemes and Associated (Directed) Graphs"],"prefix":"10.37236","volume":"32","author":[{"given":"Giusy","family":"Monzillo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Safet","family":"Penji\u0107","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,3,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i1p54\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i1p54\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T15:16:38Z","timestamp":1743088598000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i1p54"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,28]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1,17]]}},"URL":"https:\/\/doi.org\/10.37236\/12973","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,28]]},"article-number":"P1.54"}}