{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T12:13:45Z","timestamp":1767183225864,"version":"3.41.2"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:p> A restrained Italian dominating function (RIDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying: (i) [Formula: see text] for every vertex [Formula: see text] with [Formula: see text], where [Formula: see text] is the set of vertices adjacent to [Formula: see text]; (ii) the subgraph induced by the vertices assigned 0 under [Formula: see text] has no isolated vertices. The weight of an RIDF is the sum of its function values over the whole set of vertices, and the restrained Italian domination number [Formula: see text] is the minimum weight of an RIDF on [Formula: see text] In this paper, we initiate the study of the restrained Italian bondage number [Formula: see text] of a graph [Formula: see text] with no isolated vertices defined as the smallest size of set of edges [Formula: see text] for which [Formula: see text]. We begin by showing that the decision problem associated with the restrained Italian bondage problem is NP-hard. Then basic properties of the restrained Italian bondage number are presented. Finally, some sharp bounds for [Formula: see text] are also established. <\/jats:p>","DOI":"10.1142\/s1793830922501191","type":"journal-article","created":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T07:59:12Z","timestamp":1654761552000},"source":"Crossref","is-referenced-by-count":2,"title":["Restrained Italian bondage number in graphs"],"prefix":"10.1142","volume":"15","author":[{"given":"N.","family":"Ebrahimi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I. R. Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Amjadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I. R. 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