{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T20:15:27Z","timestamp":1774383327842,"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>A graph $G$ is distinguished if its vertices are labelled by a map $\\phi: V(G) \\longrightarrow \\{1,2,\\ldots, k\\}$ so that no non-trivial graph automorphism preserves $\\phi$. The distinguishing number of $G$ is the minimum number $k$ necessary for $\\phi$ to distinguish the graph. It measures the symmetry of the graph.\r\nWe extend these definitions to an arbitrary group action of $\\Gamma$ on a set $X$. A labelling $\\phi: X \\longrightarrow \\{1,2,\\ldots,k\\}$ is distinguishing if no element of $\\Gamma$ preserves $\\phi$ except those which fix each element of $X$. The distinguishing number of the group action on $X$ is the minimum $k$ needed for $\\phi$ to distinguish the group action. We show that distinguishing group actions is a more general problem than distinguishing graphs.\r\nWe completely characterize actions of $S_n$ on a set with distinguishing number $n$, answering an open question of Albertson and Collins.<\/jats:p>","DOI":"10.37236\/1816","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:32:06Z","timestamp":1578709926000},"source":"Crossref","is-referenced-by-count":23,"title":["Distinguishing Numbers for Graphs and Groups"],"prefix":"10.37236","volume":"11","author":[{"given":"Julianna","family":"Tymoczko","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,9,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r63\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r63\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:54:02Z","timestamp":1579323242000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r63"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,9,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1816","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,9,16]]},"article-number":"R63"}}