{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:19Z","timestamp":1740155959525,"version":"3.37.3"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:p>A total Steiner set of [Formula: see text] is a Steiner set [Formula: see text] such that the subgraph [Formula: see text] induced by [Formula: see text] has no isolated vertex. The minimum cardinality of a total Steiner set of [Formula: see text] is the total Steiner number of [Formula: see text] and is denoted by [Formula: see text]. Some general properties satisfied by this concept are studied. Connected graphs of order [Formula: see text] with total Steiner number 2 or 3 are characterized. We partially characterized classes of graphs of order [Formula: see text] with total Steiner number equal to [Formula: see text] or [Formula: see text] or [Formula: see text]. It is shown that [Formula: see text]. It is shown that for every pair k, p of integers with [Formula: see text], there exists a connected graph [Formula: see text] of order [Formula: see text] such that [Formula: see text]. Also, it is shown that for every positive integer [Formula: see text], [Formula: see text] and [Formula: see text] with [Formula: see text], there exists a connected graph [Formula: see text] of order [Formula: see text] such that [Formula: see text] and [Formula: see text].<\/jats:p>","DOI":"10.1142\/s179383092050038x","type":"journal-article","created":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T03:53:05Z","timestamp":1583121185000},"page":"2050038","source":"Crossref","is-referenced-by-count":3,"title":["The total Steiner number of a graph"],"prefix":"10.1142","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4715-5638","authenticated-orcid":false,"given":"J.","family":"John","sequence":"first","affiliation":[{"name":"Department of Mathematics, Government College of Engineering, Tirunelveli-627 007, India"}]}],"member":"219","published-online":{"date-parts":[[2020,6,15]]},"reference":[{"key":"S179383092050038XBIB001","doi-asserted-by":"publisher","DOI":"10.5614\/ejgta.2019.7.2.3"},{"key":"S179383092050038XBIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830914500608"},{"key":"S179383092050038XBIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830915500494"},{"volume-title":"Distance in Graphs","year":"1990","author":"Buckley F.","key":"S179383092050038XBIB004"},{"key":"S179383092050038XBIB005","doi-asserted-by":"crossref","first-page":"399","DOI":"10.21136\/CPM.1989.118395","volume":"114","author":"Chartrand G.","year":"1989","journal-title":"Casopis Pro Pestovan Matematiky"},{"key":"S179383092050038XBIB006","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00456-8"},{"key":"S179383092050038XBIB007","first-page":"65","volume":"170","author":"Eballe R.","year":"2004","journal-title":"Congres. 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