{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:43:42Z","timestamp":1760028222241,"version":"3.41.2"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"DOI":"10.13039\/501100010218","name":"Department of Science and Technology, Philippines","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100010218","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2024,10]]},"abstract":"<jats:p> Let [Formula: see text] be a finite simple graph. A set [Formula: see text] is a total hop dominating set of [Formula: see text] if for every [Formula: see text], there exists [Formula: see text] such that [Formula: see text]. Any total hop dominating set of [Formula: see text] of minimum cardinality is a [Formula: see text]-set of [Formula: see text]. A total hop dominating set [Formula: see text] of [Formula: see text] which intersects every [Formula: see text]-set of [Formula: see text] is a transversal total hop dominating set. The minimum cardinality [Formula: see text] of a transversal total hop dominating set in [Formula: see text] is the transversal total hop domination number of [Formula: see text]. In this paper, we initiate the study of transversal total hop domination in graphs. First, we characterize a graph [Formula: see text] of order [Formula: see text] for which [Formula: see text] is [Formula: see text] or [Formula: see text], and also we determine the specific values of [Formula: see text] for some special graphs [Formula: see text]. Next, we solve some realization problems involving [Formula: see text] with other parameters of [Formula: see text]. Finally, we investigate the transversal total hop domination in the complementary prism, corona, and lexicographic product of graphs. <\/jats:p>","DOI":"10.1142\/s1793830923500957","type":"journal-article","created":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T04:46:36Z","timestamp":1698554796000},"source":"Crossref","is-referenced-by-count":1,"title":["Transversal total hop domination in graphs"],"prefix":"10.1142","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-4905-6503","authenticated-orcid":false,"given":"Maria Andrea O.","family":"Bonsocan","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, CSM, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, Philippines"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-7424-8994","authenticated-orcid":false,"given":"Ferdinand P.","family":"Jamil","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, CSM, Center for Mathematical and Theoretical Physical Sciences, PRISM, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, Philippines"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,12,22]]},"reference":[{"key":"S1793830923500957BIB001","doi-asserted-by":"publisher","DOI":"10.2298\/FIL1602293A"},{"key":"S1793830923500957BIB002","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199601)21:1<21::AID-JGT3>3.0.CO;2-O"},{"key":"S1793830923500957BIB003","doi-asserted-by":"publisher","DOI":"10.56947\/gjom.v6i2.132"},{"key":"S1793830923500957BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00010-022-00896-0"},{"key":"S1793830923500957BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(91)90055-7"},{"issue":"2","key":"S1793830923500957BIB007","first-page":"179","volume":"18","author":"Arriola S.","year":"2017","journal-title":"Adv. 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