{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T05:08:08Z","timestamp":1754111288976,"version":"3.37.3"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2019,8]]},"abstract":"<jats:p> An exponential dominating set of graph [Formula: see text] is a kind of distance domination subset [Formula: see text] such that [Formula: see text], [Formula: see text], where [Formula: see text] is the length of a shortest path in [Formula: see text] if such a path exists, and [Formula: see text] otherwise. The minimum exponential domination number, [Formula: see text] is the smallest cardinality of an exponential dominating set. The minimum exponential domination number, [Formula: see text] can be decreased or increased by removal of some vertices from [Formula: see text]. In this paper, we investigate of this phenomenon which is referred to critical and stability in graphs. <\/jats:p>","DOI":"10.1142\/s0129054119500217","type":"journal-article","created":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T04:24:14Z","timestamp":1565670254000},"page":"781-791","source":"Crossref","is-referenced-by-count":4,"title":["Exponential Domination Critical and Stability in Some Graphs"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2086-8969","authenticated-orcid":false,"given":"Aysun","family":"Ayta\u00e7","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Ege University, Izmir 35100, Turkey"}]},{"given":"Bet\u00fcl","family":"Atay Atakul","sequence":"additional","affiliation":[{"name":"Department of Computer Education and Instructional Technology, Faculty of Education, A\u011fr\u0131 Ibrahim \u00c7e\u00e7en University, A\u011fr\u0131 04100, Turkey"}]}],"member":"219","published-online":{"date-parts":[[2019,8,13]]},"reference":[{"issue":"1","key":"S0129054119500217BIB001","first-page":"12","volume":"16","author":"Ayta\u00e7 A.","year":"2016","journal-title":"Nonlinear Dynamics and Systems Theory"},{"key":"S0129054119500217BIB002","first-page":"271","volume":"8","author":"Ayta\u00e7 A.","year":"2018","journal-title":"Bulletin of International Mathematical Virtual Institute"},{"issue":"2","key":"S0129054119500217BIB003","first-page":"243","volume":"8","author":"Ayta\u00e7 A.","year":"2017","journal-title":"International Journal of Nonlinear Analysis and Applications"},{"key":"S0129054119500217BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054117500277"},{"journal-title":"TWMS Journal of Applied and Engineering Mathematics","author":"Ayta\u00e7 A.","key":"S0129054119500217BIB005"},{"issue":"2","key":"S0129054119500217BIB006","first-page":"139","volume":"17","author":"Ayta\u00e7 V.","year":"2017","journal-title":"Nonlinear Dynamics and Systems Theory"},{"key":"S0129054119500217BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054117500034"},{"key":"S0129054119500217BIB008","first-page":"3","volume":"135","author":"Berberler M. 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