{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T19:17:15Z","timestamp":1649186235599},"reference-count":4,"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":"Department of Science & Technology (DST)","award":["SR\/S4\/MS:287\/05"],"award-info":[{"award-number":["SR\/S4\/MS:287\/05"]}]}],"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:mi>G<\/mml:mi><mml:mo>=<\/mml:mo><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>V<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>E<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>be a connected simple graph and let<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>M<\/mml:mi><\/mml:mrow><\/mml:math>be a nonempty subset of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>V<\/mml:mi><\/mml:mrow><\/mml:math>. The<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>M<\/mml:mi><\/mml:mrow><\/mml:math>-distance pattern of a vertex<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><\/mml:math>in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>is the set of all distances from<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><\/mml:math>to the vertices in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:mi>M<\/mml:mi><\/mml:mrow><\/mml:math>. If the distance patterns of all vertices in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:mi>V<\/mml:mi><\/mml:mrow><\/mml:math>are distinct, then the set<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:mi>M<\/mml:mi><\/mml:mrow><\/mml:math>is a distance pattern distinguishing set of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>. A graph<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>with a distance pattern distinguishing set is called a distance pattern distinguishing graph. Minimum number of vertices in a distance pattern distinguishing set is called distance pattern distinguishing number of a graph. This paper initiates a study on the problem of finding distance pattern distinguishing number of a graph and gives bounds for distance pattern distinguishing number. Further, this paper provides an algorithm to determine whether a graph is a distance pattern distinguishing graph or not and hence to determine the distance pattern distinguishing number of that graph.<\/jats:p>","DOI":"10.1155\/2014\/328703","type":"journal-article","created":{"date-parts":[[2014,6,11]],"date-time":"2014-06-11T21:21:00Z","timestamp":1402521660000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["On the Distance Pattern Distinguishing Number of a Graph"],"prefix":"10.1155","volume":"2014","author":[{"given":"Sona","family":"Jose","sequence":"first","affiliation":[{"name":"Centre for Mathematical Sciences, Pala Campus, Arunapuram, Kerala 686 574, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Germina K.","family":"Augustine","sequence":"additional","affiliation":[{"name":"Centre for Mathematical Sciences, Pala Campus, Arunapuram, Kerala 686 574, India"},{"name":"P.G. & Research Department of Mathematics, Mary Matha Arts & Science College, Kannur University, Mananthavady 670645, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"5","first-page":"549","volume":"14","year":"1975","journal-title":"Congressus Numerantium"},{"issue":"15","key":"2","first-page":"713","volume":"6","year":"2011","journal-title":"International Journal of Contemporary Mathematical Sciences"},{"issue":"1\u20133","key":"4","first-page":"99","volume":"105","year":"2000","journal-title":"Discrete Applied Mathematics"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(95)00106-2"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/328703.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/328703.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/328703.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T16:53:33Z","timestamp":1471539213000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/328703\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":4,"alternative-id":["328703","328703"],"URL":"https:\/\/doi.org\/10.1155\/2014\/328703","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}