{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:33:54Z","timestamp":1753882434869,"version":"3.41.2"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2022,5]]},"abstract":"<jats:p> For a set [Formula: see text] of vertices and a vertex [Formula: see text] in a graph [Formula: see text], the [Formula: see text]-vector [Formula: see text] is the adjacency representation of [Formula: see text] with respect to [Formula: see text], where [Formula: see text] and [Formula: see text] is the minimum of [Formula: see text] and the distance between the vertices [Formula: see text] and [Formula: see text]. The set [Formula: see text] is an adjacency resolving set for [Formula: see text] if distinct vertices of [Formula: see text] have distinct adjacency representations with respect to [Formula: see text]. The minimum cardinality of an adjacency resolving set for [Formula: see text] is its adjacency dimension. It is clear that the adjacency dimension of an [Formula: see text]-vertex graph [Formula: see text] is between [Formula: see text] and [Formula: see text]. The graphs with adjacency dimension [Formula: see text] and [Formula: see text] are known. All graphs with adjacency dimension [Formula: see text], and all [Formula: see text]-vertex graphs with adjacency dimension [Formula: see text] are studied in this paper. In terms of the diameter and order of [Formula: see text], a sharp upper bound is found for adjacency dimension of [Formula: see text]. Also, a sharp lower bound for adjacency dimension of [Formula: see text] is obtained in terms of order of [Formula: see text]. Using these two bounds, all graphs with adjacency dimension 2, and all [Formula: see text]-vertex graphs with adjacency dimension [Formula: see text] are characterized. <\/jats:p>","DOI":"10.1142\/s1793830921501342","type":"journal-article","created":{"date-parts":[[2021,4,28]],"date-time":"2021-04-28T14:14:50Z","timestamp":1619619290000},"source":"Crossref","is-referenced-by-count":1,"title":["Graphs with constant adjacency dimension"],"prefix":"10.1142","volume":"14","author":[{"given":"Mohsen","family":"Jannesari","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, Shahreza Campus, University of Isfahan, Iran"}]}],"member":"219","published-online":{"date-parts":[[2021,5,19]]},"reference":[{"key":"S1793830921501342BIB001","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdq096"},{"key":"S1793830921501342BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.11.013"},{"key":"S1793830921501342BIB003","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025745406160"},{"key":"S1793830921501342BIB004","doi-asserted-by":"publisher","DOI":"10.1137\/050641867"},{"key":"S1793830921501342BIB005","first-page":"349","volume":"88","author":"Chappell G. 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