{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T15:42:16Z","timestamp":1767109336583,"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>This work introduces the technique of using a carefully chosen determining set to prove the existence of a distinguishing labeling using few labels.  A graph $G$ is said to be $d$-distinguishable if there is a labeling of the vertex set using $1, \\ldots, d$ so that no nontrivial automorphism of $G$ preserves the labels.  A set of vertices $S\\subseteq V(G)$ is a determining set for $G$ if every automorphism of $G$ is uniquely determined by its action on $S$.  We prove that a graph is $d$-distinguishable if and only if it has a determining set that can be $(d-1)$-distinguished.  We use this to prove that every Kneser graph $K_{n:k}$ with $n\\geq 6$ and $k\\geq 2$ is $2$-distinguishable.<\/jats:p>","DOI":"10.37236\/938","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:51:49Z","timestamp":1578718309000},"source":"Crossref","is-referenced-by-count":17,"title":["Using Determining Sets to Distinguish Kneser Graphs"],"prefix":"10.37236","volume":"14","author":[{"given":"Michael O.","family":"Albertson","sequence":"first","affiliation":[]},{"given":"Debra L.","family":"Boutin","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,1,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:04:29Z","timestamp":1579320269000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/938","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,1,29]]},"article-number":"R20"}}