{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:32Z","timestamp":1740155972408,"version":"3.37.3"},"reference-count":8,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:p> A graph pebbling is a network optimization model for the transmission of consumable resources. A pebbling move on a connected graph [Formula: see text] is the process of removing two pebbles from a vertex and placing one of them on an adjacent vertex after configuration of a fixed number of pebbles on the vertex set of [Formula: see text]. The pebbling number of [Formula: see text], denoted by [Formula: see text], is defined to be the least number of pebbles to guarantee that for any configuration of pebbles on [Formula: see text] and arbitrary vertex [Formula: see text], there is a sequence of pebbling movement that places at least one pebble on [Formula: see text]. For connected graphs [Formula: see text] and [Formula: see text], Graham\u2019s conjecture asserted that [Formula: see text]. In this paper, we show that such conjecture holds when [Formula: see text] is a complete bipartite graph with sufficiently large order in terms of [Formula: see text] and the order of [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s179383091950068x","type":"journal-article","created":{"date-parts":[[2019,9,27]],"date-time":"2019-09-27T03:13:48Z","timestamp":1569554028000},"page":"1950068","source":"Crossref","is-referenced-by-count":1,"title":["Graham\u2019s pebbling conjecture holds for the product of a graph and a sufficiently large complete bipartite graph"],"prefix":"10.1142","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1889-3826","authenticated-orcid":false,"given":"Nopparat","family":"Pleanmani","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"}]}],"member":"219","published-online":{"date-parts":[[2019,12,19]]},"reference":[{"key":"S179383091950068XBIB001","doi-asserted-by":"publisher","DOI":"10.1137\/0402041"},{"key":"S179383091950068XBIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF02880130"},{"key":"S179383091950068XBIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2010.02.008"},{"key":"S179383091950068XBIB004","first-page":"15","volume":"59","author":"Herscovici D. S.","year":"2010","journal-title":"Graph Theory Notes New York"},{"key":"S179383091950068XBIB005","first-page":"1428","volume-title":"Handbook of Graph Theory","author":"Hurlbert G.","year":"2014","edition":"2"},{"volume-title":"Product Graphs","year":"2000","author":"Imrich W.","key":"S179383091950068XBIB007"},{"key":"S179383091950068XBIB009","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00177-1"},{"volume-title":"Introduction to Graph Theory","year":"1996","author":"West D.","key":"S179383091950068XBIB010"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S179383091950068X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T01:43:20Z","timestamp":1576806200000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S179383091950068X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12]]},"references-count":8,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["10.1142\/S179383091950068X"],"URL":"https:\/\/doi.org\/10.1142\/s179383091950068x","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2019,12]]}}}