{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,15]],"date-time":"2024-04-15T08:02:04Z","timestamp":1713168124556},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,2]]},"abstract":"<jats:p> Let [Formula: see text] be a connected graph of order at least two with vertex set [Formula: see text]. For [Formula: see text], let [Formula: see text] denote the length of an [Formula: see text] geodesic in [Formula: see text]. A function [Formula: see text] is called a dominating broadcast function of [Formula: see text] if, for each vertex [Formula: see text], there exists a vertex [Formula: see text] such that [Formula: see text] and [Formula: see text], and the broadcast domination number, [Formula: see text], of [Formula: see text] is the minimum of [Formula: see text] over all dominating broadcast functions [Formula: see text] of [Formula: see text]. For [Formula: see text], let [Formula: see text] denote the set of vertices [Formula: see text] such that either [Formula: see text] lies on a [Formula: see text] geodesic or [Formula: see text] lies on a [Formula: see text] geodesic of [Formula: see text]. Let [Formula: see text] be a function and, for any [Formula: see text], let [Formula: see text]. We say that [Formula: see text] is a strong resolving function of [Formula: see text] if [Formula: see text] for every pair of distinct vertices [Formula: see text], and the strong metric dimension, [Formula: see text], of [Formula: see text] is the minimum of [Formula: see text] over all strong resolving functions [Formula: see text] of [Formula: see text]. For any connected graph [Formula: see text], we show that [Formula: see text]; we characterize [Formula: see text] satisfying [Formula: see text] equals two and three, respectively, and characterize unicyclic graphs achieving [Formula: see text]. For any tree [Formula: see text] of order at least three, we show that [Formula: see text], and characterize trees achieving equality. Moreover, for a tree [Formula: see text] of order [Formula: see text], we obtain the results that [Formula: see text] if [Formula: see text] is central, and that [Formula: see text] if [Formula: see text] is bicentral; in each case, we characterize trees achieving equality. We conclude this paper with some remarks and an open problem. <\/jats:p>","DOI":"10.1142\/s179383092050010x","type":"journal-article","created":{"date-parts":[[2019,10,31]],"date-time":"2019-10-31T06:42:46Z","timestamp":1572504166000},"page":"2050010","source":"Crossref","is-referenced-by-count":1,"title":["Bounds on the sum of broadcast domination number and strong metric dimension of graphs"],"prefix":"10.1142","volume":"12","author":[{"given":"Eunjeong","family":"Yi","sequence":"first","affiliation":[{"name":"Texas A&M University at Galveston, Galveston, TX 77553, USA"}]}],"member":"219","published-online":{"date-parts":[[2020,1,10]]},"reference":[{"key":"S179383092050010XBIB002","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.2006.884015"},{"key":"S179383092050010XBIB003","first-page":"55","volume":"169","author":"Blair J. R. S.","year":"2004","journal-title":"Congr. Numer."},{"key":"S179383092050010XBIB005","first-page":"89","volume":"42","author":"Erwin D. 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