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For a tree [Formula: see text] of order at least two, we show that [Formula: see text], where [Formula: see text] denotes the number of exterior major vertices of [Formula: see text]; further, we characterize trees [Formula: see text] achieving equality. For a connected graph [Formula: see text] of order [Formula: see text], Bagheri Gh. et al. proved that [Formula: see text] and equality holds if and only if [Formula: see text] for [Formula: see text] and [Formula: see text], where [Formula: see text] denotes the complete graph and [Formula: see text] denotes a complete bi-partite graph of order [Formula: see text]. We characterize graphs [Formula: see text] for which [Formula: see text] equals two and three, respectively. We also characterize graphs [Formula: see text] satisfying [Formula: see text] when [Formula: see text] is a tree, a unicyclic graph, or a complete multi-partite graph.<\/jats:p>","DOI":"10.1142\/s1793830918500660","type":"journal-article","created":{"date-parts":[[2018,8,13]],"date-time":"2018-08-13T09:18:54Z","timestamp":1534151934000},"page":"1850066","source":"Crossref","is-referenced-by-count":4,"title":["Bounds on the sum of domination number and metric dimension of graphs"],"prefix":"10.1142","volume":"10","author":[{"given":"Cong X.","family":"Kang","sequence":"first","affiliation":[{"name":"Texas A&amp;M University at Galveston, Galveston, TX 77553, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eunjeong","family":"Yi","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University at Galveston, Galveston, TX 77553, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,10,11]]},"reference":[{"key":"S1793830918500660BIB002","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdq096"},{"key":"S1793830918500660BIB003","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.2006.884015"},{"key":"S1793830918500660BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(00)00198-0"},{"key":"S1793830918500660BIB005","first-page":"47","volume":"160","author":"Chartrand G.","year":"2003","journal-title":"Congr. 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