{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:46:55Z","timestamp":1759063615096,"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 labeling $f: V(G) \\rightarrow \\{1, 2, \\ldots, d\\}$ of the vertex set of a graph $G$ is said to be proper $d$-distinguishing if it is a proper coloring of $G$ and any nontrivial automorphism of $G$ maps at least one vertex to a vertex with a different label. The distinguishing chromatic number of $G$, denoted by $\\chi_D(G)$, is the minimum $d$ such that $G$ has a proper $d$-distinguishing labeling. Let $\\chi(G)$ be the chromatic number of $G$ and $D(G)$ be the distinguishing number of $G$. Clearly, $\\chi_D(G) \\ge \\chi(G)$ and $\\chi_D(G) \\ge D(G)$. Collins, Hovey and Trenk have given a tight upper bound on $\\chi_D(G)-\\chi(G)$ in terms of the order of the automorphism group of $G$, improved when the automorphism group of $G$ is a finite abelian group. The Kneser graph $K(n,r)$ is a graph whose vertices are the $r$-subsets of an $n$ element set, and two vertices of $K(n,r)$ are adjacent if their corresponding two $r$-subsets are disjoint. In this paper, we provide a class of graphs $G$, namely Kneser graphs $K(n,r)$, whose automorphism group is the symmetric group, $S_n$, such that $\\chi_D(G) - \\chi(G) \\le 1$. In particular, we prove that $\\chi_D(K(n,2))=\\chi(K(n,2))+1$ for $n\\ge 5$. In addition, we show that $\\chi_D(K(n,r))=\\chi(K(n,r))$ for $n \\ge 2r+1$ and $r\\ge 3$.<\/jats:p>","DOI":"10.37236\/3066","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:00:10Z","timestamp":1578711610000},"source":"Crossref","is-referenced-by-count":3,"title":["The Distinguishing Chromatic Number of Kneser Graphs"],"prefix":"10.37236","volume":"20","author":[{"given":"Zhongyuan","family":"Che","sequence":"first","affiliation":[]},{"given":"Karen L.","family":"Collins","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,1,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p23\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:27:30Z","timestamp":1579260450000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/3066","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,1,29]]},"article-number":"P23"}}