{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T04:22:41Z","timestamp":1666844561277},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,10]]},"abstract":"<jats:p>The [Formula: see text]-pebbling number, [Formula: see text], of a connected graph [Formula: see text], is the smallest positive integer such that from every placement of [Formula: see text] pebbles, [Formula: see text] pebbles can be moved to any specified target vertex by a sequence of pebbling moves, each move taking two pebbles off a vertex and placing one on an adjacent vertex. A graph [Formula: see text] satisfies the [Formula: see text]-pebbling property if [Formula: see text] pebbles can be moved to any specified vertex when the total starting number of pebbles is [Formula: see text], where [Formula: see text] is the number of vertices with at least one pebble. We show that the cycle [Formula: see text] satisfies the [Formula: see text]-pebbling property. Herscovici conjectured that for any connected graphs [Formula: see text] and [Formula: see text], [Formula: see text]. We prove Herscovici\u2019s conjecture is true, when [Formula: see text] is an even cycle and for variety of graphs [Formula: see text] which satisfy the [Formula: see text]-pebbling property.<\/jats:p>","DOI":"10.1142\/s1793830920500718","type":"journal-article","created":{"date-parts":[[2020,6,4]],"date-time":"2020-06-04T03:25:45Z","timestamp":1591241145000},"page":"2050071","source":"Crossref","is-referenced-by-count":0,"title":["Herscovici\u2019s conjecture on C2n \u00d7 G"],"prefix":"10.1142","volume":"12","author":[{"given":"A.","family":"Lourdusamy","sequence":"first","affiliation":[{"name":"Department of Mathematics, St. Xavier\u2019s College (Autonomous), Palayamkottai - 627 002, India"}]},{"given":"T.","family":"Mathivanan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, St. Xavier\u2019s College (Autonomous), Palayamkottai - 627 002, India"}]}],"member":"219","published-online":{"date-parts":[[2020,7,1]]},"reference":[{"key":"S1793830920500718BIB001","doi-asserted-by":"publisher","DOI":"10.1137\/0402041"},{"key":"S1793830920500718BIB002","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10080"},{"key":"S1793830920500718BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2012.03.032"},{"key":"S1793830920500718BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(97)00229-X"},{"issue":"7","key":"S1793830920500718BIB005","first-page":"999","volume":"161","author":"Yin J.-H.","year":"2013","journal-title":"Discr. 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