{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:28:20Z","timestamp":1740144500188,"version":"3.37.3"},"reference-count":21,"publisher":"EDP Sciences","issue":"5","license":[{"start":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T00:00:00Z","timestamp":1570579200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.edpsciences.org\/en\/authors\/copyright-and-licensing"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2018,9,4]]},"published-print":{"date-parts":[[2019,11]]},"abstract":"<jats:p>The stability of a communication network has a great importance in network design. There are several vulnerability measures used to determine the resistance of network to the disruption in this sense. Domination theory provides a model to measure the vulnerability of a graph network. A new vulnerability measure of domination integrity was introduced by Sundareswaran in his Ph.D. thesis (Parameters of vulnerability in graphs (2010)) and defined as DI(<jats:italic>G<\/jats:italic>)\u00a0=\u00a0min{|<jats:italic>S<\/jats:italic>|\u00a0+\u00a0<jats:italic>m<\/jats:italic>(<jats:italic>G<\/jats:italic>\u00a0\u2212\u00a0<jats:italic>S<\/jats:italic>):<jats:italic>S<\/jats:italic> \u2208 <jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>)} where <jats:italic>m<\/jats:italic>(<jats:italic>G<\/jats:italic>\u00a0\u2212\u00a0<jats:italic>S<\/jats:italic>) denotes the order of a largest component of graph <jats:italic>G<\/jats:italic>\u00a0\u2212\u00a0<jats:italic>S<\/jats:italic> and <jats:italic>S<\/jats:italic> is a dominating set of <jats:italic>G<\/jats:italic>. The domination integrity of an undirected connected graph is such a measure that works on the whole graph and also the remaining components of graph after any break down. Here we determine the domination integrity of wheel graph <jats:italic>W<\/jats:italic><jats:sub>1,<jats:italic>n<\/jats:italic><\/jats:sub>, Ladder graph <jats:italic>L<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, <jats:italic>S<\/jats:italic><jats:sub><jats:italic>m,n<\/jats:italic><\/jats:sub>, Friendship graph <jats:italic>F<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, Thorn graph of <jats:italic>P<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> and <jats:italic>C<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> which are commonly used graph models in network design.<\/jats:p>","DOI":"10.1051\/ro\/2018074","type":"journal-article","created":{"date-parts":[[2018,9,6]],"date-time":"2018-09-06T10:03:27Z","timestamp":1536228207000},"page":"1721-1728","source":"Crossref","is-referenced-by-count":1,"title":["Domination integrity of some graph classes"],"prefix":"10.1051","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3980-196X","authenticated-orcid":false,"given":"Ayse","family":"Besirik","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1074-5589","authenticated-orcid":false,"given":"Elgin","family":"Kilic","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2019,10,9]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0166-218X(92)90122-Q","volume":"37\/38","author":"Bagga","year":"1992","journal-title":"Discrete Appl. 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