{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:48:57Z","timestamp":1759063737242,"version":"3.37.3"},"reference-count":8,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100005276","name":"National Board for Higher Mathematics","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100005276","id-type":"DOI","asserted-by":"publisher"}]},{"name":"DST FIST"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,8]]},"abstract":"<jats:p> A vertex [Formula: see text] of a graph [Formula: see text] is said to [Formula: see text]-dominate every edge incident to [Formula: see text], as well as every edge adjacent to these incident edges. A set [Formula: see text] is a vertex-edge dominating set (double vertex-edge dominating set, respectively) if every edge of [Formula: see text] is [Formula: see text]-dominated by at least one vertex (at least two vertices) of [Formula: see text] The minimum cardinality of a vertex-edge dominating set (double vertex-edge dominating set, respectively) of [Formula: see text] is the vertex-edge domination number [Formula: see text] (the double vertex-edge domination number [Formula: see text], respectively). In this paper, we initiate the study of double vertex-edge domination. We first show that determining the number [Formula: see text] for bipartite graphs is NP-complete. We also prove that for every nontrivial connected graphs [Formula: see text] [Formula: see text] and we characterize the trees [Formula: see text] with [Formula: see text] or [Formula: see text] Finally, we provide two lower bounds on the double ve-domination number of trees and unicycle graphs in terms of\u00a0the order [Formula: see text] the number of leaves and support vertices, and we characterize the trees attaining the lower bound. <\/jats:p>","DOI":"10.1142\/s1793830917500458","type":"journal-article","created":{"date-parts":[[2017,6,19]],"date-time":"2017-06-19T07:09:27Z","timestamp":1497856167000},"page":"1750045","source":"Crossref","is-referenced-by-count":20,"title":["Double vertex-edge domination"],"prefix":"10.1142","volume":"09","author":[{"given":"Balakrishna","family":"Krishnakumari","sequence":"first","affiliation":[{"name":"Department of Mathematics, SASTRA University, Tanjore, Tamilnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mustapha","family":"Chellali","sequence":"additional","affiliation":[{"name":"LAMDA-RO Laboratory, Department of Mathematics, University of Blida B. P. 270, Blida, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanamandram B.","family":"Venkatakrishnan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, SASTRA University, Tanjore, Tamilnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2017,8,16]]},"reference":[{"key":"S1793830917500458BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s00010-015-0354-2"},{"key":"S1793830917500458BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2014.06.016"},{"key":"S1793830917500458BIB003","first-page":"283","volume-title":"Graph Theory with Applications to Algorithms and Computer Science","author":"Fink J.","year":"1985"},{"volume-title":"Fundamentals of Domination in Graphs","year":"1998","author":"Haynes T. W.","key":"S1793830917500458BIB004"},{"volume-title":"Domination in Graphs: Advanced Topics","year":"1998","author":"Haynes T. 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Math."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830917500458","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,1]],"date-time":"2019-10-01T18:38:55Z","timestamp":1569955135000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830917500458"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8]]},"references-count":8,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2017,8,16]]},"published-print":{"date-parts":[[2017,8]]}},"alternative-id":["10.1142\/S1793830917500458"],"URL":"https:\/\/doi.org\/10.1142\/s1793830917500458","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2017,8]]}}}