{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:33:31Z","timestamp":1753882411257,"version":"3.41.2"},"reference-count":7,"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":[[2021,10]]},"abstract":"<jats:p> Let [Formula: see text] be a graph. A Roman[Formula: see text]-dominating function [Formula: see text] has the property that for every vertex [Formula: see text] with [Formula: see text], either [Formula: see text] is adjacent to a vertex assigned [Formula: see text] under [Formula: see text], or [Formula: see text] is adjacent to at least two vertices assigned [Formula: see text] under [Formula: see text]. A set [Formula: see text] of distinct Roman [Formula: see text]-dominating functions on [Formula: see text] with the property that [Formula: see text] for each [Formula: see text] is called a Roman[Formula: see text]-domination family (or functions) on [Formula: see text]. The maximum number of functions in a Roman [Formula: see text]-dominating family on [Formula: see text] is the Roman[Formula: see text]-domatic number of [Formula: see text], denoted by [Formula: see text]. In this paper, we answer two conjectures of Volkman [L. Volkmann, The Roman [Formula: see text]-domatic number of graphs, Discrete Appl. Math.\u00a0258 (2019) 235\u2013241] about Roman [Formula: see text]-domatic number of graphs and we study this parameter for join of graphs and complete bipartite graphs. <\/jats:p>","DOI":"10.1142\/s179383092150052x","type":"journal-article","created":{"date-parts":[[2020,11,3]],"date-time":"2020-11-03T14:40:35Z","timestamp":1604414435000},"source":"Crossref","is-referenced-by-count":1,"title":["On the Roman {2}-domatic number of graphs"],"prefix":"10.1142","volume":"13","author":[{"given":"A.","family":"Giahtazeh","sequence":"first","affiliation":[{"name":"Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P. O. Box 14115-137, Tehran, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9020-0871","authenticated-orcid":false,"given":"H. R.","family":"Maimani","sequence":"additional","affiliation":[{"name":"Mathematics Section, Department of Basic Sciences, Shahid Rajaee Teacher Training University, P. O. Box 16785-163, Tehran, Iran"}]},{"given":"A.","family":"Iranmanesh","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P. O. Box 14115-137, Tehran, Iran"}]}],"member":"219","published-online":{"date-parts":[[2020,12,11]]},"reference":[{"key":"S179383092150052XBIB002","doi-asserted-by":"publisher","DOI":"10.1201\/b19731"},{"key":"S179383092150052XBIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2015.11.013"},{"key":"S179383092150052XBIB004","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230070305"},{"key":"S179383092150052XBIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2003.06.004"},{"key":"S179383092150052XBIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2016.09.035"},{"key":"S179383092150052XBIB007","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican1299-136"},{"key":"S179383092150052XBIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2018.11.027"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S179383092150052X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,14]],"date-time":"2021-10-14T03:59:44Z","timestamp":1634183984000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S179383092150052X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,11]]},"references-count":7,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["10.1142\/S179383092150052X"],"URL":"https:\/\/doi.org\/10.1142\/s179383092150052x","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2020,12,11]]},"article-number":"2150052"}}