{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T10:39:52Z","timestamp":1774435192386,"version":"3.50.1"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:p>Let [Formula: see text] be a simple graph. An independent double Roman dominating function (IDRDF) on a graph [Formula: see text] is a function [Formula: see text] having the property that first if [Formula: see text], then vertex [Formula: see text] has at least two neighbors assigned [Formula: see text] under [Formula: see text] or one neighbor [Formula: see text] with [Formula: see text]; second if [Formula: see text], then vertex [Formula: see text] must have at least one neighbor [Formula: see text] with [Formula: see text] and third the set of vertices assigned with positive numbers is independent. The weight of an IDRDF [Formula: see text] is equal to [Formula: see text]. The independent double Roman domination number [Formula: see text] is the minimum weight among all IDRDFs of [Formula: see text]. A subset [Formula: see text] of [Formula: see text] is a 2-independent set of [Formula: see text] if every vertex of [Formula: see text] has at most one neighbor in [Formula: see text]. The maximum cardinality of a 2-independent set of [Formula: see text] is the 2-independence number [Formula: see text]. In this paper, it is shown that both parameters are incomparable, in general. Also, we prove that if [Formula: see text] is a tree, then [Formula: see text]. Moreover, all extremal trees attaining equality are characterized.<\/jats:p>","DOI":"10.1142\/s1793830925500478","type":"journal-article","created":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T22:02:32Z","timestamp":1740780152000},"source":"Crossref","is-referenced-by-count":0,"title":["Independent double roman domination number of a tree in terms of its 2-independence number"],"prefix":"10.1142","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-9726-069X","authenticated-orcid":false,"given":"Halimeh","family":"Koulivand","sequence":"first","affiliation":[{"name":"Department of Mathematics, Tafresh University, Tafresh, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1317-1434","authenticated-orcid":false,"given":"Mohammad","family":"Habibi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Tafresh University, Tafresh, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8781-6704","authenticated-orcid":false,"given":"Hassan","family":"Arianpoor","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Tafresh University, Tafresh, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-0565-4446","authenticated-orcid":false,"given":"Mina","family":"Valinavaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,4,19]]},"reference":[{"key":"S1793830925500478BIB001","doi-asserted-by":"publisher","DOI":"10.2298\/AADM160802017A"},{"key":"S1793830925500478BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830918500520"},{"key":"S1793830925500478BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-011-1040-3"},{"key":"S1793830925500478BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2003.06.004"},{"key":"S1793830925500478BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(85)90040-1"},{"key":"S1793830925500478BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.09.043"},{"key":"S1793830925500478BIB007","first-page":"301","volume-title":"Graph Theory with Applications to Algorithms and Computer Science","author":"Fink J. F.","year":"1985"},{"key":"S1793830925500478BIB008","unstructured":"I. Gorodezky, Domination sets in Kneser graphs, Dr. Sci. Thesis, University of Waterloo, Waterloo, Ontario, Canada (2007)."},{"key":"S1793830925500478BIB009","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"S1793830925500478BIB010","volume-title":"Domination in Graphs: Advanced Topics","author":"Haynes T. W.","year":"1998"},{"key":"S1793830925500478BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/0165-4896(88)90041-8"},{"key":"S1793830925500478BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s41980-019-00274-8"},{"key":"S1793830925500478BIB013","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830917500239"},{"key":"S1793830925500478BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s41980-019-00300-9"},{"key":"S1793830925500478BIB015","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.2000.12005243"},{"key":"S1793830925500478BIB016","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican1299-136"},{"key":"S1793830925500478BIB017","doi-asserted-by":"publisher","DOI":"10.1080\/00207160.2012.742513"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830925500478","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T08:01:35Z","timestamp":1774425695000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830925500478"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,19]]},"references-count":17,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["10.1142\/S1793830925500478"],"URL":"https:\/\/doi.org\/10.1142\/s1793830925500478","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,19]]},"article-number":"2550047"}}