{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:23:07Z","timestamp":1759335787570,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A graph $G$ is said to be 2-distinguishable if there is a labeling of the vertices with two\u00a0labels such that only the trivial automorphism preserves the labels. Call the minimum size of\u00a0a label class in such a labeling of $G$ the cost of 2-distinguishing $G$.We show that the connected, locally finite, infinite graphs with finite 2-distinguishing cost are exactly the graphs with countable automorphism group. Further we show that in such graphs the cost is less than three times the size of a smallest determining set. We also another, sharper bound on the 2-distinguishing cost, in particular for graphs of linear growth.<\/jats:p>","DOI":"10.37236\/4263","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:33:50Z","timestamp":1578702830000},"source":"Crossref","is-referenced-by-count":2,"title":["Infinite Graphs with Finite 2-Distinguishing Cost"],"prefix":"10.37236","volume":"21","author":[{"given":"Debra","family":"Boutin","sequence":"first","affiliation":[]},{"given":"Wilfried","family":"Imrich","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,12,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i4p52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i4p52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:39:20Z","timestamp":1579257560000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i4p52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,11]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4263","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,12,11]]},"article-number":"P4.52"}}