{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T10:17:56Z","timestamp":1774347476279,"version":"3.50.1"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T00:00:00Z","timestamp":1774310400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T00:00:00Z","timestamp":1774310400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1007\/s40314-026-03719-z","type":"journal-article","created":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T06:40:13Z","timestamp":1774334413000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the total outer-independent domination number of subdivision graphs"],"prefix":"10.1007","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2806-4842","authenticated-orcid":false,"given":"Abel","family":"Cabrera-Mart\u00ednez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ismael","family":"Rios-Villamar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Omar Rosario","family":"Cayetano","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 M.","family":"Sigarreta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,3,24]]},"reference":[{"key":"3719_CR1","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1007\/s00009-022-02236-7","volume":"20","author":"S Bermudo","year":"2023","unstructured":"Bermudo S (2023) Total domination on tree operators. Mediterr J Math 20:42","journal-title":"Mediterr J Math"},{"issue":"18","key":"3719_CR2","doi-asserted-by":"publisher","first-page":"6581","DOI":"10.2298\/FIL2418581C","volume":"38","author":"A Cabrera Mart\u00ednez","year":"2024","unstructured":"Cabrera Mart\u00ednez A (2024) Total outer-independent domination in regular graphs. Filomat 38(18):6581\u20136586","journal-title":"Filomat"},{"key":"3719_CR3","doi-asserted-by":"publisher","first-page":"153","DOI":"10.33044\/revuma.1652","volume":"63","author":"A Cabrera Mart\u00ednez","year":"2022","unstructured":"Cabrera Mart\u00ednez A, Cabrera Garc\u00eda S, Peterin I, Yero IG (2022) The total co-independent domination number of some graph operations. Rev de la Union Mat Argentina 63:153\u2013168","journal-title":"Rev de la Union Mat Argentina"},{"issue":"3","key":"3719_CR4","doi-asserted-by":"publisher","first-page":"184","DOI":"10.55016\/ojs\/cdm.v19i3.75096","volume":"19","author":"A Cabrera Mart\u00ednez","year":"2024","unstructured":"Cabrera Mart\u00ednez A, Hern\u00e1ndez FA, Sigarreta JM, Yero IG (2024) A note on total co-independent domination in trees. Contrib Discrete Math 19(3):184\u2013195","journal-title":"Contrib Discrete Math"},{"key":"3719_CR5","doi-asserted-by":"publisher","first-page":"933","DOI":"10.7151\/dmgt.2478","volume":"44","author":"A Cabrera Mart\u00ednez","year":"2024","unstructured":"Cabrera Mart\u00ednez A, S\u00e1nchez JL, Sigarreta JM (2024) On the total domination number of total graphs. Discuss Math Graph Theory 44:933\u2013951","journal-title":"Discuss Math Graph Theory"},{"key":"3719_CR6","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1007\/s40840-025-02016-y","volume":"49","author":"A Cabrera Mart\u00ednez","year":"2026","unstructured":"Cabrera Mart\u00ednez A, Rios-Villamar I, Reyna Hern\u00e1ndez G, Sigarreta JM (2026) On the double total domination number of some graph operators. Bull Malays Math Sci Soc 49:18","journal-title":"Bull Malays Math Sci Soc"},{"key":"3719_CR7","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1002\/net.3230100304","volume":"10","author":"EJ Cockayne","year":"1980","unstructured":"Cockayne EJ, Dawes RM, Hedetniemi ST (1980) Total domination in graphs. Networks 10:211\u2013219","journal-title":"Networks"},{"key":"3719_CR8","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/j.dam.2025.12.055","volume":"384","author":"E De Jes\u00fas S\u00e1nchez","year":"2026","unstructured":"De Jes\u00fas S\u00e1nchez E, Cabrera Mart\u00ednez A, Rios Villamar I, Sigarreta JM (2026) On the (total) domination in subdivision graphs. Discrete Appl Math 384:201\u2013210","journal-title":"Discrete Appl Math"},{"key":"3719_CR9","unstructured":"Haynes TW, Hedetniemi ST, Slater PJ (1998) Fundamentals of domination in graphs. Chapman and Hall\/CRC Pure and Applied Mathematics Series, Marcel Dekker, Inc., New York"},{"key":"3719_CR10","doi-asserted-by":"publisher","first-page":"665","DOI":"10.7151\/dmgt.2454","volume":"42","author":"MA Henning","year":"2022","unstructured":"Henning MA (2022) Bounds on domination parameters in graphs: a brief survey. Discuss Math Graph Theory 42:665\u2013708","journal-title":"Discuss Math Graph Theory"},{"key":"3719_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-6525-6","volume-title":"Total domination in graphs","author":"MA Henning","year":"2013","unstructured":"Henning MA, Yeo A (2013) Total domination in graphs. Springer, New York"},{"key":"3719_CR12","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1016\/j.crma.2010.11.021","volume":"349","author":"M Krzywkowski","year":"2011","unstructured":"Krzywkowski M (2011) A lower bound on the total outer-independent domination number of a tree. Compt Rend Math 349:7\u20139","journal-title":"Compt Rend Math"},{"key":"3719_CR13","doi-asserted-by":"publisher","first-page":"153","DOI":"10.7494\/OpMath.2012.32.1.153","volume":"32","author":"M Krzywkowski","year":"2012","unstructured":"Krzywkowski M (2012) An upper bound on the total outer-independent domination number of a tree. Opus Math 32:153\u2013158","journal-title":"Opus Math"},{"key":"3719_CR14","doi-asserted-by":"publisher","first-page":"35544","DOI":"10.1109\/ACCESS.2018.2851972","volume":"6","author":"Z Li","year":"2018","unstructured":"Li Z, Shao Z, Lang F, Zhang X, Liu J-B (2018) Computational complexity of outer-independent total and total Roman domination numbers in trees. IEEE Access 6:35544\u201335550","journal-title":"IEEE Access"},{"key":"3719_CR15","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.dam.2021.01.027","volume":"294","author":"DA Mojdeh","year":"2021","unstructured":"Mojdeh DA, Peterin I, Samadi B, Yero IG (2021) On three outer-independent domination related parameters in graphs. Discrete Appl Math 294:115\u2013124","journal-title":"Discrete Appl Math"},{"key":"3719_CR16","doi-asserted-by":"publisher","first-page":"241","DOI":"10.3390\/math9030241","volume":"9","author":"JM Sigarreta","year":"2021","unstructured":"Sigarreta JM (2021) Total domination on some graph operators. Mathematics 9:241","journal-title":"Mathematics"},{"key":"3719_CR17","first-page":"129","volume":"6","author":"ND Soner","year":"2012","unstructured":"Soner ND, Dhananjaya Murthy BV, Deepak G (2012) Total co-independent domination in graphs. Appl Math Sci 6:129\u2013132","journal-title":"Appl Math Sci"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-026-03719-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-026-03719-z","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-026-03719-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T06:40:17Z","timestamp":1774334417000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-026-03719-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,24]]},"references-count":17,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2026,9]]}},"alternative-id":["3719"],"URL":"https:\/\/doi.org\/10.1007\/s40314-026-03719-z","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,24]]},"assertion":[{"value":"25 October 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 January 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 March 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"315"}}