{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:22Z","timestamp":1753893862629,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$. A locating-total dominating set of $G$ is a total dominating set $D$ of $G$ with the additional property that every two distinct vertices outside $D$ have distinct neighbors in $D$; that is, for distinct vertices $u$ and $v$ outside $D$, $N(u) \\cap D \\ne N(v) \\cap D$ where $N(u)$ denotes the open neighborhood of $u$. A graph is twin-free if every two distinct vertices have distinct open and closed neighborhoods. \u00a0The location-total domination number of $G$, denoted $\\gamma_t^L(G)$, is the minimum cardinality of a locating-total dominating set in $G$. It is well-known that every connected graph of order $n \\ge 3$ has a total dominating set of size at most $\\frac{2}{3}n$. We conjecture that if $G$ is a twin-free graph of order $n$ with no isolated vertex, then $\\gamma_t^L(G) \\le \\frac{2}{3}n$. We prove the conjecture for graphs without $4$-cycles as a subgraph. We also prove that if $G$ is a twin-free graph of order $n$, then $\\gamma_t^L(G) \\le \\frac{3}{4}n$.<\/jats:p>","DOI":"10.37236\/5147","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:46:56Z","timestamp":1578689216000},"source":"Crossref","is-referenced-by-count":2,"title":["Locating-Total Dominating Sets in Twin-Free Graphs: a Conjecture"],"prefix":"10.37236","volume":"23","author":[{"given":"Florent","family":"Foucaud","sequence":"first","affiliation":[]},{"given":"Michael A.","family":"Henning","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,7,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:18:21Z","timestamp":1579238301000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i3p9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,22]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,7,8]]}},"URL":"https:\/\/doi.org\/10.37236\/5147","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,7,22]]},"article-number":"P3.9"}}