{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T01:18:05Z","timestamp":1649207885696},"reference-count":8,"publisher":"Hindawi Limited","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":[{"name":"TSNC of China","award":["TSA1013"],"award-info":[{"award-number":["TSA1013"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Let<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u039b<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>be the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>-dimensional Fibonacci cube and Lucas cube, respectively. Denote by<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><mml:mo stretchy=\"false\">[<\/mml:mo><mml:msub><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>z<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">]<\/mml:mo><\/mml:math>the subgraph of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>induced by the end-vertex<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:msub><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>z<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>that has no up-neighbor. In this paper, the number of end-vertices and domination number<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:mi>\u03b3<\/mml:mi><\/mml:mrow><\/mml:math>of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u039b<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>are studied. The formula of calculating the number of end-vertices is given and it is proved that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mi>\u03b3<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><mml:mo stretchy=\"false\">[<\/mml:mo><mml:msub><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>z<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">]<\/mml:mo><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>\u2264<\/mml:mo><mml:msup><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><mml:mo>-<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo>+<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>. Using these results, the larger bound on the domination number<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mrow><mml:mi>\u03b3<\/mml:mi><\/mml:mrow><\/mml:math>of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u039b<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>is determined.<\/jats:p>","DOI":"10.1155\/2014\/954738","type":"journal-article","created":{"date-parts":[[2014,3,4]],"date-time":"2014-03-04T21:10:54Z","timestamp":1393967454000},"page":"1-5","source":"Crossref","is-referenced-by-count":0,"title":["The Larger Bound on the Domination Number of Fibonacci Cubes and Lucas Cubes"],"prefix":"10.1155","volume":"2014","author":[{"given":"Shengzhang","family":"Ren","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Shaanxi University of Technology Hanzhong, Shaanxi 723001, China"},{"name":"Department of Mathematics, Lanzhou University Lanzhou, Gansu 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"5","doi-asserted-by":"publisher","DOI":"10.1109\/71.205649"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(01)00387-9"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.03.012"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.11.006"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(01)00407-1"},{"key":"7","first-page":"433","volume":"80","year":"2012","journal-title":"Journal of Combinatorial Mathematics and Combinatorial Computing"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(02)00824-5"},{"key":"1","year":"1976"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/954738.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/954738.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/954738.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,29]],"date-time":"2016-07-29T11:44:36Z","timestamp":1469792676000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/954738\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":8,"alternative-id":["954738","954738"],"URL":"https:\/\/doi.org\/10.1155\/2014\/954738","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}