{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:21:45Z","timestamp":1753885305290,"version":"3.41.2"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"JSPS","award":["19K14493"],"award-info":[{"award-number":["19K14493"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:p> A total dominator coloring of a graph G is a proper coloring of G in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic number of a graph is the minimum number of color classes in a total dominator coloring. In this paper, we study the total dominator coloring on middle graphs by giving several bounds for the case of general graphs and trees. Moreover, we calculate explicitly the total dominator chromatic number of the middle graph of several known families of graphs. <\/jats:p>","DOI":"10.1142\/s1793830922500768","type":"journal-article","created":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T16:40:44Z","timestamp":1649781644000},"source":"Crossref","is-referenced-by-count":4,"title":["Total dominator coloring number of middle graphs"],"prefix":"10.1142","volume":"15","author":[{"given":"Farshad","family":"Kazemnejad","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Basic Sciences, Ilam University, P. O. Box 69315-516, Ilam, Iran"}]},{"given":"Behnaz","family":"Pahlavsay","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo 060-0810, Japan"}]},{"given":"Elisa","family":"Palezzato","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo 060-0810, Japan"}]},{"given":"Michele","family":"Torielli","sequence":"additional","affiliation":[{"name":"Department of Mathematics, GI-CoRE GSB, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo 060-0810, Japan"}]}],"member":"219","published-online":{"date-parts":[[2022,4,11]]},"reference":[{"doi-asserted-by":"publisher","key":"S1793830922500768BIB001","DOI":"10.1142\/1280"},{"doi-asserted-by":"publisher","key":"S1793830922500768BIB002","DOI":"10.1016\/0012-365X(76)90037-6"},{"volume-title":"Fundamentals Domination in Graphs","year":"1998","author":"Haynes T. W.","key":"S1793830922500768BIB003"},{"volume-title":"Domination in Graphs: Advanced Topics","year":"1998","author":"Haynes T. W.","key":"S1793830922500768BIB004"},{"doi-asserted-by":"publisher","key":"S1793830922500768BIB005","DOI":"10.1007\/s00373-014-1425-1"},{"doi-asserted-by":"publisher","key":"S1793830922500768BIB006","DOI":"10.1007\/978-1-4614-6525-6"},{"issue":"2","key":"S1793830922500768BIB007","first-page":"57","volume":"4","author":"Kazemi A. P.","year":"2015","journal-title":"Trans. Combin."},{"key":"S1793830922500768BIB014","doi-asserted-by":"crossref","first-page":"15","DOI":"10.7151\/dmgt.2242","volume":"42","author":"Pahlavsay B.","year":"2022","journal-title":"Discuss. Math. Graph Theory"},{"issue":"3","key":"S1793830922500768BIB015","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1007\/s00373-021-02297-7","volume":"37","author":"Pahlavsay B.","year":"2021","journal-title":"Graphs Combin."},{"key":"S1793830922500768BIB016","volume-title":"Introduction to Graph Theory","author":"West D. B.","year":"2001","edition":"2"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922500768","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,2]],"date-time":"2023-03-02T03:02:01Z","timestamp":1677726121000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922500768"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,11]]},"references-count":10,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["10.1142\/S1793830922500768"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922500768","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2022,4,11]]},"article-number":"2250076"}}