{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T04:11:29Z","timestamp":1754107889417},"reference-count":31,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2018,11]]},"abstract":"<jats:p>Let [Formula: see text] be a graph and [Formula: see text]. We define by [Formula: see text] the subgraph of [Formula: see text] induced by [Formula: see text]. For each vertex [Formula: see text] and for each vertex [Formula: see text], [Formula: see text] is the length of the shortest path in [Formula: see text] between [Formula: see text] and [Formula: see text] if such a path exists, and [Formula: see text] otherwise. For a vertex [Formula: see text], let [Formula: see text] where [Formula: see text]. J\u00e4ger and Rautenbach [27] define a set [Formula: see text] of vertices to be exponential independent if [Formula: see text] for every vertex [Formula: see text] in [Formula: see text]. The exponential independence number [Formula: see text] of [Formula: see text] is the maximum order of an exponential independent set. In this paper, we give a general theorem and we examine exponential independence number of some tree graphs and thorn graph of some graphs.<\/jats:p>","DOI":"10.1142\/s0129054118500260","type":"journal-article","created":{"date-parts":[[2018,11,12]],"date-time":"2018-11-12T04:18:10Z","timestamp":1541996290000},"page":"1151-1164","source":"Crossref","is-referenced-by-count":2,"title":["Exponential Independence Number of Some Graphs"],"prefix":"10.1142","volume":"29","author":[{"given":"Canan","family":"\u00c7ift\u00e7i","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Sciences, Ordu University, 52200 Ordu, Turkey"}]},{"given":"Aysun","family":"Ayta\u00e7","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey"}]}],"member":"219","published-online":{"date-parts":[[2018,11,11]]},"reference":[{"key":"S0129054118500260BIB001","first-page":"12","volume":"16","author":"Ayta\u00e7 A.","year":"2016","journal-title":"Nonlinear Dynamics and Systems Theory"},{"key":"S0129054118500260BIB002","doi-asserted-by":"publisher","DOI":"10.1134\/S0001434613050180"},{"key":"S0129054118500260BIB003","author":"Aytac A.","year":"2017","journal-title":"International Journal of Foundations of Computer Science"},{"key":"S0129054118500260BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S012905411000726X"},{"key":"S0129054118500260BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054111008660"},{"key":"S0129054118500260BIB006","author":"Aytac A.","year":"2016","journal-title":"RAIRO \u2014 Operations Research"},{"issue":"7","key":"S0129054118500260BIB007","first-page":"925","volume":"64","author":"Aytac A.","year":"2011","journal-title":"Comptes Rendus de L Academie Bulgare des Sciences"},{"key":"S0129054118500260BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054115500379"},{"issue":"1","key":"S0129054118500260BIB009","first-page":"107","volume":"10","author":"Ayta\u00e7 V.","year":"2009","journal-title":"Selcuk Journal of Applied Mathematics"},{"key":"S0129054118500260BIB010","first-page":"1665","volume":"65","author":"Ayta\u00e7 V.","year":"2012","journal-title":"CR Lacad. Bulg. Sci."},{"key":"S0129054118500260BIB011","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054117500034"},{"issue":"1","key":"S0129054118500260BIB012","first-page":"137","volume":"55","author":"Aytac V.","year":"2009","journal-title":"International Journal of Pure and Applied Mathematics"},{"issue":"2","key":"S0129054118500260BIB013","first-page":"139","volume":"17","author":"Ayta\u00e7 V.","year":"2017","journal-title":"Nonlinear Dynamics and Systems Theory"},{"key":"S0129054118500260BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(92)90122-Q"},{"issue":"38","key":"S0129054118500260BIB015","first-page":"13","volume":"1","author":"Barefoot C. A.","year":"1987","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"S0129054118500260BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90085-7"},{"key":"S0129054118500260BIB017","first-page":"3","volume":"135","author":"Berberler M. E.","year":"2017","journal-title":"ARS Combinatoria"},{"key":"S0129054118500260BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"S0129054118500260BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(73)90138-6"},{"key":"S0129054118500260BIB020","first-page":"605","volume":"66","author":"Cygan M.","year":"2011","journal-title":"MATCH Communications in Mathematical and in Computer Chemistry"},{"key":"S0129054118500260BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.06.040"},{"key":"S0129054118500260BIB022","first-page":"47","volume-title":"Annals of Discrete Mathematics","volume":"48","author":"Fink J. F.","year":"1991"},{"key":"S0129054118500260BIB023","doi-asserted-by":"publisher","DOI":"10.1109\/TCOM.1970.1090419"},{"key":"S0129054118500260BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(79)90132-8"},{"issue":"31","key":"S0129054118500260BIB025","first-page":"73","volume":"63","author":"Gutman I.","year":"1998","journal-title":"Publ. Inst. Math. (Beograd)"},{"key":"S0129054118500260BIB026","volume-title":"Domination in Graphs: Advanced Topics","author":"Haynes T. W.","year":"1997"},{"key":"S0129054118500260BIB027","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2016.10.018"},{"issue":"3","key":"S0129054118500260BIB028","first-page":"315","volume":"65","author":"Odabas Z. N.","year":"2012","journal-title":"Comptes Rendus de L Academie Bulgare des Sciences"},{"issue":"3","key":"S0129054118500260BIB029","doi-asserted-by":"crossref","first-page":"297","DOI":"10.3233\/FI-2013-835","volume":"124","author":"Odaba\u015f Z. N.","year":"2013","journal-title":"Fundamenta Informaticae"},{"key":"S0129054118500260BIB030","doi-asserted-by":"publisher","DOI":"10.3390\/mca21030029"},{"key":"S0129054118500260BIB031","doi-asserted-by":"publisher","DOI":"10.1051\/ro\/2015062"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054118500260","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,15]],"date-time":"2020-11-15T01:42:13Z","timestamp":1605404533000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054118500260"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11]]},"references-count":31,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2018,11,11]]},"published-print":{"date-parts":[[2018,11]]}},"alternative-id":["10.1142\/S0129054118500260"],"URL":"https:\/\/doi.org\/10.1142\/s0129054118500260","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11]]}}}