{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T10:58:39Z","timestamp":1717585119374},"reference-count":10,"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\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>For a vertex<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>v<\/mml:mi><\/mml:mrow><\/mml:math>of a 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>, the<jats:italic>lower connectivity<\/jats:italic>, denoted by<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:msub><mml:mrow><mml:mi>s<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>v<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>G<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, is the smallest number of vertices that contains<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>v<\/mml:mi><\/mml:mrow><\/mml:math>and those vertices whose deletion from<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>produces a disconnected or a trivial graph. The average lower connectivity denoted by<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:msub><mml:mrow><mml:mi>\u03ba<\/mml:mi><\/mml:mrow><mml:mrow><mml:mtext>a<\/mml:mtext><mml:mtext>v<\/mml:mtext><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>G<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>is the value<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:msub><mml:mo stretchy=\"false\">\u2211<\/mml:mo><mml:mrow><mml:mi>v<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mi>V<\/mml:mi><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:msub><mml:mrow><mml:msub><mml:mrow><mml:mi>s<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>v<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><mml:mo>\/<\/mml:mo><mml:mfenced open=\"|\" close=\"|\" separators=\"|\"><mml:mrow><mml:mi>V<\/mml:mi><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mfenced><\/mml:math>. It is shown that this parameter can be used to measure the vulnerability of networks. This paper contains results on bounds for the average lower connectivity and obtains the average lower connectivity of some graphs.<\/jats:p>","DOI":"10.1155\/2014\/807834","type":"journal-article","created":{"date-parts":[[2014,2,12]],"date-time":"2014-02-12T21:05:59Z","timestamp":1392239159000},"page":"1-4","source":"Crossref","is-referenced-by-count":4,"title":["The Average Lower Connectivity of Graphs"],"prefix":"10.1155","volume":"2014","author":[{"given":"Ersin","family":"Aslan","sequence":"first","affiliation":[{"name":"Turgutlu Vocational Training School, Celal Bayar University, Turgutlu, Manisa 45400, Turkey"}]}],"member":"98","reference":[{"issue":"11","key":"1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0895-7177(93)90246-U","volume":"17","year":"1993","journal-title":"Mathematical and Computer Modelling"},{"key":"20","first-page":"231","volume":"116","year":"1996","journal-title":"Congressus Numerantium"},{"key":"15","first-page":"305","volume":"71","year":"2004","journal-title":"Ars Combinatoria"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(01)00180-7"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.06.035"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.03.051"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190130603"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(87)90151-8"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(02)00572-3"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(98)10041-3"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/807834.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/807834.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/807834.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T07:46:47Z","timestamp":1498117607000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/807834\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":10,"alternative-id":["807834","807834"],"URL":"https:\/\/doi.org\/10.1155\/2014\/807834","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}