{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T17:25:15Z","timestamp":1761845115127,"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>A coloring of the vertices of a graph $G$ is said to be distinguishing provided that no nontrivial automorphism of $G$ preserves all of the vertex colors. The distinguishing number of $G$, denoted $D(G)$, is the minimum number of colors in a distinguishing coloring of $G$. The distinguishing number, first introduced by Albertson and Collins in 1996, has been widely studied and a number of interesting results exist throughout the literature.   In this paper, the notion of distinguishing colorings is extended to that of list-distinguishing colorings. Given a family $L=\\{L(v)\\}_{v\\in V(G)}$ of lists assigning available colors to the vertices of $G$, we say that $G$ is $L$-distinguishable if there is a distinguishing coloring $f$ of $G$ such that $f(v)\\in L(v)$ for all $v$. The list-distinguishing number of $G$, $D_{\\ell}(G)$, is the minimum integer $k$ such that $G$ is $L$-distinguishable for any assignment $L$ of lists with $|L(v)|=k$ for all $v$.  Here, we determine the list-distinguishing number for several families of graphs and highlight a number of distinctions between the problems of distinguishing and list-distinguishing a graph.     <\/jats:p>","DOI":"10.37236\/648","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:43:18Z","timestamp":1578714198000},"source":"Crossref","is-referenced-by-count":6,"title":["List-Distinguishing Colorings of Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"Michael","family":"Ferrara","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Breeann","family":"Flesch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ellen","family":"Gethner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,8,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p161\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p161\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:07:20Z","timestamp":1579302440000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p161"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,8,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/648","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,8,5]]},"article-number":"P161"}}