{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:09:11Z","timestamp":1753884551058,"version":"3.41.2"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11701157"],"award-info":[{"award-number":["11701157"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:p>Let [Formula: see text] be an edge-colored graph with order [Formula: see text] and [Formula: see text] be a fixed integer satisfying [Formula: see text]. For a vertex set [Formula: see text] of at least two vertices, a tree containing the vertices of [Formula: see text] in [Formula: see text] is called an [Formula: see text]-tree. The [Formula: see text]-tree [Formula: see text] is a total-rainbow [Formula: see text]-tree if the elements of [Formula: see text], except for the vertex set [Formula: see text], have distinct colors. A total-colored graph [Formula: see text] is said to be total-rainbow [Formula: see text]-tree connected if for every set [Formula: see text] of [Formula: see text] vertices in [Formula: see text], there exists a total-rainbow [Formula: see text]-tree in [Formula: see text], while the total-coloring of [Formula: see text] is called a [Formula: see text]-total-rainbow coloring. The [Formula: see text]-total-rainbow index of a nontrivial connected graph [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed in a [Formula: see text]-total-rainbow coloring of [Formula: see text]. In this paper, we show a sharp upper bound for [Formula: see text], where [Formula: see text] is a [Formula: see text]-connected or [Formula: see text]-edge-connected graph.<\/jats:p>","DOI":"10.1142\/s0219265921420019","type":"journal-article","created":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T04:42:41Z","timestamp":1624250561000},"source":"Crossref","is-referenced-by-count":0,"title":["Tight Upper Bound of the 3-Total-Rainbow Index for 2-(Edge-)Connected Graphs"],"prefix":"10.1142","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0380-9468","authenticated-orcid":false,"given":"Yingbin","family":"Ma","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, P. R. 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