{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T15:32:35Z","timestamp":1649086355814},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2016,9]]},"abstract":"<jats:p> For a simple graph [Formula: see text] and for a pair of vertices [Formula: see text], we say that a vertex [Formula: see text] resolves [Formula: see text] and [Formula: see text] if the shortest path from [Formula: see text] to [Formula: see text] is of a different length than the shortest path from [Formula: see text] to [Formula: see text]. A set of vertices [Formula: see text] is a resolving set if for every pair of vertices [Formula: see text] and [Formula: see text] in [Formula: see text], there exists a vertex [Formula: see text] that resolves [Formula: see text] and [Formula: see text]. The minimum weight resolving set problem is to find a resolving set [Formula: see text] for a weighted graph [Formula: see text] such that [Formula: see text] is minimum, where [Formula: see text] is the weight of vertex [Formula: see text]. In this paper, we explore the possible solutions of this problem for grid graphs [Formula: see text] where [Formula: see text]. We give a complete characterization of solutions whose cardinalities are 2 or 3, and show that the maximum cardinality of a solution is [Formula: see text]. We show that the grid has the property that given a landmark set, we only need to investigate whether or not all pairs of vertices that share common neighbors are resolved to determine if the whole graph is resolved. We use this result to provide a characterization of a class of minimals whose cardinalities range from [Formula: see text] to [Formula: see text] and show that the number of such minimals is [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830916500488","type":"journal-article","created":{"date-parts":[[2016,5,30]],"date-time":"2016-05-30T12:04:27Z","timestamp":1464609867000},"page":"1650048","source":"Crossref","is-referenced-by-count":0,"title":["Minimum weight resolving sets of grid graphs"],"prefix":"10.1142","volume":"08","author":[{"given":"Patrick","family":"Andersen","sequence":"first","affiliation":[{"name":"School of Mathematics and Physical Sciences, University of Newcastle, University Dr, Callaghan, New South Wales 2308, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cyriac","family":"Grigorious","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physical Sciences, University of Newcastle, University Dr, Callaghan, New South Wales 2308, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mirka","family":"Miller","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physical Sciences, University of Newcastle, University Dr, Callaghan, New South Wales 2308, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,8]]},"reference":[{"key":"S1793830916500488BIB001","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.2006.884015"},{"key":"S1793830916500488BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(00)00198-0"},{"key":"S1793830916500488BIB003","first-page":"47","volume":"160","author":"Chartrand G.","year":"2003","journal-title":"Congr. 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