{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:00:13Z","timestamp":1746802813358,"version":"3.40.5"},"reference-count":17,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001321","name":"National Research Foundation","doi-asserted-by":"publisher","award":["2012R1A1A20 05115","2013000416"],"award-info":[{"award-number":["2012R1A1A20 05115","2013000416"]}],"id":[{"id":"10.13039\/501100001321","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001321","name":"National Research Foundation","doi-asserted-by":"publisher","award":["2012R1A1A20 05115","2013000416"],"award-info":[{"award-number":["2012R1A1A20 05115","2013000416"]}],"id":[{"id":"10.13039\/501100001321","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>Graph bundles generalize the notion of covering graphs and graph products. Graph bundles have been applied in computer architecture and communication networks. The bondage number is an important parameter for measuring the vulnerability and stability of the network domination under link failure. The bondage number<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>b<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>G<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>of a graph<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>is the minimum number of edges whose removal enlarges the domination number. In this paper, we show that the bondage number of every<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>4<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>bundles over a cycle<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:msub><mml:mi>C<\/mml:mi><mml:mi>n<\/mml:mi><\/mml:msub><mml:mrow><mml:mo>\u2009\u2009(<\/mml:mo><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>\u2265<\/mml:mo><mml:mn>4<\/mml:mn><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>is equal to 4.<\/jats:p>","DOI":"10.1155\/2013\/520251","type":"journal-article","created":{"date-parts":[[2013,12,11]],"date-time":"2013-12-11T16:02:05Z","timestamp":1386777725000},"page":"1-5","source":"Crossref","is-referenced-by-count":0,"title":["Bondage Numbers of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>4<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>Bundles over a Cycle<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>"],"prefix":"10.1155","volume":"2013","author":[{"given":"Moo Young","family":"Sohn","sequence":"first","affiliation":[{"name":"Mathematics, Changwon National University, Changwon 641-773, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fu-Tao","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Anhui University, Hefei 230601, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaeun","family":"Lee","sequence":"additional","affiliation":[{"name":"Mathematics, Yeungnam University, Kyongsan 712-749, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"volume":"10","year":"2003","series-title":"Network Theory and Applications","key":"18"},{"year":"1998","key":"5"},{"volume":"209","year":"1998","key":"6"},{"doi-asserted-by":"publisher","key":"4","DOI":"10.1016\/0012-365X(90)90348-L"},{"doi-asserted-by":"publisher","key":"7","DOI":"10.1016\/j.jco.2011.11.001"},{"volume":"2013","year":"2013","journal-title":"International Journal of Combinatorics","key":"19"},{"doi-asserted-by":"publisher","key":"8","DOI":"10.1007\/s11464-012-0173-x"},{"key":"3","series-title":"Monographs and Textbooks in Pure and Applied Mathematics","first-page":"471","volume-title":"Bondage, insensitivity, and reinforcement","volume":"209","year":"1998"},{"doi-asserted-by":"publisher","key":"16","DOI":"10.4134\/JKMS.2007.44.6.1213"},{"doi-asserted-by":"publisher","key":"13","DOI":"10.1016\/j.disc.2004.12.019"},{"doi-asserted-by":"publisher","key":"10","DOI":"10.1016\/j.disc.2007.03.027"},{"key":"2","first-page":"299","volume":"97","year":"2010","journal-title":"Ars Combinatoria"},{"doi-asserted-by":"publisher","key":"11","DOI":"10.4153\/CJM-1990-039-3"},{"key":"20","first-page":"30","volume":"9","year":"1963","journal-title":"Vy\u010disl Sistemy"},{"doi-asserted-by":"publisher","key":"1","DOI":"10.1002\/jgt.20565"},{"doi-asserted-by":"publisher","key":"21","DOI":"10.1007\/BF02896459"},{"doi-asserted-by":"publisher","key":"12","DOI":"10.1016\/0166-218X(93)E0167-W"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/520251.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/520251.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/520251.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T10:28:10Z","timestamp":1469874490000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/520251\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":17,"alternative-id":["520251","520251"],"URL":"https:\/\/doi.org\/10.1155\/2013\/520251","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}