{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T16:57:13Z","timestamp":1789664233741,"version":"4.0.1"},"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>In this paper the problem of constructing graphs having a $(1,\\le \\ell)$-identifying code of small cardinality is addressed. It is known that the cardinality of such a code is bounded by $\\Omega\\left({\\ell^2\\over\\log \\ell}\\log n\\right)$. Here we construct graphs on $n$ vertices having a $(1,\\le \\ell)$-identifying code of cardinality $O\\left(\\ell^4 \\log n\\right)$ for all $\\ell \\ge 2$. We derive our construction from a connection between identifying codes and superimposed codes, which we describe in this paper.<\/jats:p>","DOI":"10.37236\/1910","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:19:02Z","timestamp":1578701942000},"source":"Crossref","is-referenced-by-count":17,"title":["Construction of Codes Identifying Sets of Vertices"],"prefix":"10.37236","volume":"12","author":[{"given":"Sylvain","family":"Gravier","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julien","family":"Moncel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2005,3,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r13\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:50:56Z","timestamp":1579305056000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1910","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,3,8]]},"article-number":"R13"}}