{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:49Z","timestamp":1740134569379,"version":"3.37.3"},"reference-count":9,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["10971248","1408085MA08","KJ2013Z279"],"award-info":[{"award-number":["10971248","1408085MA08","KJ2013Z279"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003995","name":"Anhui Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["10971248","1408085MA08","KJ2013Z279"],"award-info":[{"award-number":["10971248","1408085MA08","KJ2013Z279"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003995","name":"Anhui Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["10971248","1408085MA08","KJ2013Z279"],"award-info":[{"award-number":["10971248","1408085MA08","KJ2013Z279"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>A pebbling move on a graph<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>consists of taking two pebbles off one vertex and placing one pebble on an adjacent vertex. The pebbling number of a connected graph<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>, denoted by<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>G<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, is the least<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>such that any distribution of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>pebbles on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>allows one pebble to be moved to any specified but arbitrary vertex by a sequence of pebbling moves. This paper determines the pebbling numbers and the 2-pebbling property of the middle graph of fan graphs.<\/jats:p>","DOI":"10.1155\/2014\/304514","type":"journal-article","created":{"date-parts":[[2014,7,22]],"date-time":"2014-07-22T21:04:03Z","timestamp":1406063043000},"page":"1-5","source":"Crossref","is-referenced-by-count":0,"title":["The 2-Pebbling Property of the Middle Graph of Fan Graphs"],"prefix":"10.1155","volume":"2014","author":[{"given":"Yongsheng","family":"Ye","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Huaibei Normal University, Huaibei, Anhui 235000, China"}]},{"given":"Fang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Huaibei Normal University, Huaibei, Anhui 235000, China"}]},{"given":"Caixia","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Huaibei Normal University, Huaibei, Anhui 235000, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1137\/0402041"},{"issue":"2","key":"6","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/PL00021179","volume":"16","year":"2000","journal-title":"Graphs and Combinatorics"},{"issue":"5","key":"4","first-page":"907","volume":"30","year":"2006","journal-title":"Southeast Asian Bulletin of Mathematics"},{"issue":"4","key":"3","first-page":"125","volume":"32","year":"2006","journal-title":"Journal of Dalian Maritime University"},{"key":"5","first-page":"65","volume":"107","year":"1995","journal-title":"Congressus Numerantium"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2012.07.013"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2012.07.016"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02872335"},{"issue":"3","key":"7","first-page":"35","volume":"17","year":"2013","journal-title":"Operations Research Transactions"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/304514.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/304514.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/304514.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,15]],"date-time":"2023-07-15T12:04:04Z","timestamp":1689422644000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/304514\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":9,"alternative-id":["304514","304514"],"URL":"https:\/\/doi.org\/10.1155\/2014\/304514","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}