{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T15:13:36Z","timestamp":1770909216141,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $R$ be a ring with identity. The\u00a0unitary Cayley graph of a ring $R$, denoted by $G_{R}$, is the graph, whose vertex set is $R$, and in which $\\{x,y\\}$ is an edge if and only if $x-y$ is a unit of $R$. In this paper we find chromatic, clique and independence number of $G_{R}$, where $R$ is a finite ring. Also, we prove that if $G_{R} \\simeq G_{S}$, then $G_{R\/J_{R}} \\simeq G_{S\/J_{S}}$, where $\\rm J_{R}$ and $\\rm J_{S}$ are Jacobson radicals of $R$ and $S$, respectively. Moreover, we prove if $G_{R} \\simeq G_{M_{n}(F)}$ then $R\\simeq M_{n}(F)$, where $R$ is a ring and $F$ is a finite field. Finally, let $R$ and $S$ be finite commutative rings, we show that if $G_{R} \\simeq G_{S}$, then $\\rm R\/ {J}_{R}\\simeq S\/J_{S}$.<\/jats:p>","DOI":"10.37236\/2214","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:35:01Z","timestamp":1578710101000},"source":"Crossref","is-referenced-by-count":23,"title":["On the Unitary Cayley Graph of a Ring"],"prefix":"10.37236","volume":"19","author":[{"given":"Dariush","family":"Kiani","sequence":"first","affiliation":[]},{"given":"Mohsen","family":"Molla Haji Aghaei","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,4,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i2p10\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i2p10\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T17:36:23Z","timestamp":1579282583000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i2p10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4,16]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2012,4,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2214","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,4,16]]},"article-number":"P10"}}