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Initially, we explore the optimality criterion for a subtree that is a center subtree within a tree network. Using this criterion, we frame the corresponding problem as a piecewise linear optimization problem. Lastly, we propose a combinatorial algorithm that effectively solves the problem in [Formula: see text] time, where [Formula: see text] represents the number of vertices in the tree.<\/jats:p>","DOI":"10.1142\/s1793830925500302","type":"journal-article","created":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T05:03:12Z","timestamp":1738731792000},"source":"Crossref","is-referenced-by-count":0,"title":["The inverse center subtree problem on tree graphs"],"prefix":"10.1142","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7522-4557","authenticated-orcid":false,"given":"Kien Trung","family":"Nguyen","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Informatics, Teacher College, Can Tho University, Can Tho, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-1990-3522","authenticated-orcid":false,"given":"Huong","family":"Nguyen-Thu","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Informatics, Teacher College, Can Tho University, Can Tho, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-2389-9437","authenticated-orcid":false,"given":"Nguyen Thanh","family":"Luan","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam"},{"name":"Vietnam National University, Ho Chi Minh City, Vietnam"},{"name":"Faculty of Basic Sciences, Vinh Long University of Technology Education, Vinh Long, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,3,18]]},"reference":[{"key":"S1793830925500302BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0217595918500306"},{"key":"S1793830925500302BIB002","doi-asserted-by":"publisher","DOI":"10.1287\/opre.49.5.771.10607"},{"key":"S1793830925500302BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2020.125078"},{"key":"S1793830925500302BIB004","doi-asserted-by":"publisher","DOI":"10.1002\/net.20427"},{"key":"S1793830925500302BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2011.01.009"},{"key":"S1793830925500302BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-009-0070-7"},{"key":"S1793830925500302BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.disopt.2004.03.003"},{"key":"S1793830925500302BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.disopt.2006.11.008"},{"key":"S1793830925500302BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585693"},{"key":"S1793830925500302BIB010","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008360312607"},{"key":"S1793830925500302BIB011","author":"Chan T. 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