{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:28:51Z","timestamp":1740144531844,"version":"3.37.3"},"reference-count":21,"publisher":"EDP Sciences","issue":"4","license":[{"start":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T00:00:00Z","timestamp":1658707200000},"content-version":"vor","delay-in-days":24,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2022,6,20]]},"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:p>Let <jats:italic>G<\/jats:italic> be a graph with vertex set <jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>). A total Italian dominating function (TIDF) on a graph <jats:italic>G<\/jats:italic> is a function <jats:italic>f<\/jats:italic>\u00a0:\u00a0<jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>)\u00a0\u2192\u00a0{0,\u00a01,\u00a02} such that (i) every vertex <jats:italic>v<\/jats:italic> with <jats:italic>f<\/jats:italic>(<jats:italic>v<\/jats:italic>) = 0 is adjacent to a vertex <jats:italic>u<\/jats:italic> with <jats:italic>f<\/jats:italic>(<jats:italic>u<\/jats:italic>) = 2 or to two vertices <jats:italic>w<\/jats:italic> and <jats:italic>z<\/jats:italic> with <jats:italic>f<\/jats:italic>(<jats:italic>w<\/jats:italic>) = <jats:italic>f<\/jats:italic>(<jats:italic>z<\/jats:italic>) = 1, and (ii) every vertex <jats:italic>v<\/jats:italic> with <jats:italic>f<\/jats:italic>(<jats:italic>v<\/jats:italic>) \u2265 1 is adjacent to a vertex <jats:italic>u<\/jats:italic> with <jats:italic>f<\/jats:italic>(<jats:italic>u<\/jats:italic>) \u2265 1. The total Italian domination number <jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>tI<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>) on a graph <jats:italic>G<\/jats:italic> is the minimum weight of a total Italian dominating function. In this paper, we present Nordhaus\u2013Gaddum type inequalities for the total Italian domination number.<\/jats:p>","DOI":"10.1051\/ro\/2022108","type":"journal-article","created":{"date-parts":[[2022,6,23]],"date-time":"2022-06-23T08:00:17Z","timestamp":1655971217000},"page":"2235-2243","source":"Crossref","is-referenced-by-count":3,"title":["Nordhaus\u2013Gaddum type inequalities on the total Italian domination number in graphs"],"prefix":"10.1051","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2298-4744","authenticated-orcid":false,"given":"Seyed Mahmoud","family":"Sheikholeslami","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lutz","family":"Volkmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2022,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"501","DOI":"10.2298\/AADM160802017A","volume":"10","author":"Abdollahzadeh Ahangar","year":"2016","journal-title":"Appl. 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