{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T04:27:42Z","timestamp":1754108862593,"version":"3.37.3"},"reference-count":26,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100006013","name":"United Arab Emirates University","doi-asserted-by":"publisher","award":["G00002233"],"award-info":[{"award-number":["G00002233"]}],"id":[{"id":"10.13039\/501100006013","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2018,2]]},"abstract":"<jats:p> Let [Formula: see text] be a connected graph and [Formula: see text] be the distance between the vertices [Formula: see text] and [Formula: see text] in [Formula: see text]. The diameter of [Formula: see text] is defined as [Formula: see text] and is denoted by [Formula: see text]. A subset of vertices [Formula: see text] is called a resolving set for [Formula: see text] if for every two distinct vertices [Formula: see text], there is a vertex [Formula: see text], [Formula: see text], such that [Formula: see text]. A resolving set containing the minimum number of vertices is called a metric basis for [Formula: see text] and the number of vertices in a metric basis is its metric dimension, denoted by [Formula: see text]. Metric dimension is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). <\/jats:p><jats:p> Let [Formula: see text] be a family of connected graphs [Formula: see text] depending on [Formula: see text] as follows: the order [Formula: see text] and [Formula: see text]. If there exists a constant [Formula: see text] such that [Formula: see text] for every [Formula: see text] then we shall say that [Formula: see text] has bounded metric dimension, otherwise [Formula: see text] has unbounded metric dimension. If all graphs in [Formula: see text] have the same metric dimension, then [Formula: see text] is called a family of graphs with constant metric dimension. <\/jats:p><jats:p> In this paper, we study the metric properties of an infinite class of circulant graphs with three generators denoted by [Formula: see text] for any positive integer [Formula: see text] and when [Formula: see text]. We compute the diameter and determine the exact value of the metric dimension of these circulant graphs. <\/jats:p>","DOI":"10.1142\/s1793830918500088","type":"journal-article","created":{"date-parts":[[2017,11,23]],"date-time":"2017-11-23T21:56:44Z","timestamp":1511474204000},"page":"1850008","source":"Crossref","is-referenced-by-count":8,"title":["On the metric dimension and diameter of circulant graphs with three jumps"],"prefix":"10.1142","volume":"10","author":[{"given":"Muhammad","family":"Imran","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, UAE"},{"name":"School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. 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