{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T18:58:14Z","timestamp":1778871494281,"version":"3.51.4"},"reference-count":18,"publisher":"EDP Sciences","issue":"1","license":[{"start":{"date-parts":[[2025,1,16]],"date-time":"2025-01-16T00:00:00Z","timestamp":1736985600000},"content-version":"vor","delay-in-days":15,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2024,12,6]]},"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>In this work we deal with three variants of domination in graphs, these are Italian domination (or Roman {2}-domination), {2}-domination and 2-domination. We define Sicilian graphs as those graphs for which the Italian domination and the {2}-domination numbers coincide. Sicilian graphs constitute a superclass of Italian graphs (introduced by Klostermeyer and MacGillivray [<jats:italic>J. Comb. Math. Comb. Comput<\/jats:italic>. 108 (2019) 125\u2013146]). First, we give a characterization of Italian graphs in terms of the existence of a special Roman {2}-dominating function. Then, we focus on web graphs for which their {2}-domination number was recently found (Cheng <jats:italic>et al<\/jats:italic>., <jats:italic>Discrete Math. Algorithms App<\/jats:italic>. 12 (2020) 2050055), and we study Sicilian web graphs. We explore also Sicilian co-bipartite graphs. As a by-product, we find the 2-domination number for web graphs and co-bipartite graphs. Finally, we show necessary conditions for non-Italian graphs to be Sicilian as well as characterize Sicilian graphs within some relevant graph classes such as quasi-threshold graphs and cographs.<\/jats:p>","DOI":"10.1051\/ro\/2024218","type":"journal-article","created":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T08:47:38Z","timestamp":1733734058000},"page":"239-249","source":"Crossref","is-referenced-by-count":1,"title":["Characterizations of Italian graphs and Sicilian graphs"],"prefix":"10.1051","volume":"59","author":[{"given":"Alberto Jos\u00e9","family":"Ferrari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valeria","family":"Leoni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mar\u00eda In\u00e9s","family":"Lopez Pujato","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2025,1,16]]},"reference":[{"key":"R1","unstructured":"Baghirova N., Gonzalez C.L., Ries B. and Schindl D., Locally checkable problems parameterized by Clique-Width, in 33rd International Symposium on Algorithms and Computation (ISAAC 2022). 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