{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T06:13:05Z","timestamp":1780380785558,"version":"3.54.1"},"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>A set of vertices $S$ resolves a connected graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The metric dimension of $G$ is the minimum cardinality of a resolving set of $G$. Let ${\\cal G}_{\\beta,D}$ be the set of graphs with metric dimension $\\beta$ and diameter $D$. It is well-known that the minimum order of a graph in ${\\cal G}_{\\beta,D}$ is exactly $\\beta+D$. The first contribution of this paper is to characterise the graphs in ${\\cal G}_{\\beta,D}$ with order $\\beta+D$ for all values of $\\beta$ and $D$. Such a characterisation was previously only known for $D\\leq2$ or $\\beta\\leq1$. The second contribution is to determine the maximum order of a graph in ${\\cal G}_{\\beta,D}$ for all values of $D$ and $\\beta$. Only a weak upper bound was previously known.<\/jats:p>","DOI":"10.37236\/302","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:16:40Z","timestamp":1578716200000},"source":"Crossref","is-referenced-by-count":96,"title":["Extremal Graph Theory for Metric Dimension and Diameter"],"prefix":"10.37236","volume":"17","author":[{"given":"Carmen","family":"Hernando","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Merc\u00e8","family":"Mora","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ignacio M.","family":"Pelayo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carlos","family":"Seara","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David R.","family":"Wood","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2010,2,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r30\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:59:01Z","timestamp":1579305541000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,2,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/302","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,2,22]]},"article-number":"R30"}}