{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:09:11Z","timestamp":1753880951410,"version":"3.41.2"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2024,5]]},"abstract":"<jats:p> A double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying (i) if [Formula: see text] then there must be at least two neighbors assigned two under [Formula: see text] or one neighbor [Formula: see text] with [Formula: see text]; and (ii) if [Formula: see text] then [Formula: see text] must be adjacent to a vertex [Formula: see text] such that [Formula: see text]. A DRDF is an outer-independent total double Roman dominating function (OITDRDF) on [Formula: see text] if the set of vertices labeled [Formula: see text] induces an edgeless subgraph and the subgraph induced by the vertices with a non-zero label has no isolated vertices. The weight of an OITDRDF is the sum of its function values over all vertices, and the outer-independent total Roman domination number [Formula: see text] is the minimum weight of an OITDRDF on [Formula: see text]. In this paper, we establish various bounds on [Formula: see text]. In particular, we present Nordhaus\u2013Gaddum-type inequalities for this parameter. Some of our results improve the previous results. <\/jats:p>","DOI":"10.1142\/s179383092350043x","type":"journal-article","created":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T03:41:37Z","timestamp":1683258097000},"source":"Crossref","is-referenced-by-count":0,"title":["New bounds on the outer-independent total double Roman domination number"],"prefix":"10.1142","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2298-4744","authenticated-orcid":false,"given":"S. M.","family":"Sheikholeslami","sequence":"first","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I. R. 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