{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,23]],"date-time":"2023-05-23T04:38:05Z","timestamp":1684816685433},"reference-count":14,"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 graph. A vertex [Formula: see text] strongly (weakly) b-dominates block [Formula: see text] if [Formula: see text] ([Formula: see text]) for every vertex [Formula: see text] in the block [Formula: see text]. A set [Formula: see text] is said to be strong (weak) vb-dominating set (SVBD-set) (WVBD-set) if every block in [Formula: see text] is strongly (weakly) b-dominated by some vertex in [Formula: see text]. The strong (weak) vb-domination number [Formula: see text] ([Formula: see text]) is the order of a minimum SVBD (WVBD) set of [Formula: see text]. A set [Formula: see text] is said to be strong (weak) vertex block independent set (SVBI-set (WVBI-set)) if [Formula: see text] is a vertex block independent set and for every vertex [Formula: see text] and every block [Formula: see text] incident on [Formula: see text], there exists a vertex [Formula: see text] in the block [Formula: see text] such that [Formula: see text] ([Formula: see text]). The strong (weak) vb-independence number [Formula: see text] ([Formula: see text]) is the cardinality of a maximum strong (weak) vertex block independent set (SVBI-set) (WVBI-set) of [Formula: see text]. In this paper, we investigate some relationships between these four parameters. Several upper and lower bounds are established. In addition, we characterize the graphs attaining some of the bounds. <\/jats:p>","DOI":"10.1142\/s1793830920500020","type":"journal-article","created":{"date-parts":[[2019,10,11]],"date-time":"2019-10-11T10:27:05Z","timestamp":1570789625000},"page":"2050002","source":"Crossref","is-referenced-by-count":2,"title":["Strong vb-dominating and vb-independent sets of a graph"],"prefix":"10.1142","volume":"12","author":[{"given":"Sayinath","family":"Udupa","sequence":"first","affiliation":[{"name":"Department of Mathematics, Manipal Institute of Technology, A Constituent unit of Manipal Academy of Higher Education-Manipal, Karnataka 576104, India"}]},{"given":"R. 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