{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:07:40Z","timestamp":1753880860254,"version":"3.41.2"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/100009110","name":"Natural Science Foundation of Xinjiang Province","doi-asserted-by":"publisher","award":["2020D04046"],"award-info":[{"award-number":["2020D04046"]}],"id":[{"id":"10.13039\/100009110","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12261085"],"award-info":[{"award-number":["12261085"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:p> A strong digraph [Formula: see text] is strongly Menger (arc) connected if, for [Formula: see text], [Formula: see text] can reach [Formula: see text] by min[Formula: see text] internally (arc) disjoint-directed paths. A digraph [Formula: see text] is [Formula: see text](-arc)-fault-tolerant strongly Menger([Formula: see text]-(A)FTSM, for short) (arc) connected if [Formula: see text] is strongly Menger (arc) connected for every [Formula: see text](respectively, [Formula: see text]) with [Formula: see text]. A digraph [Formula: see text] is [Formula: see text]-conditional (arc)-fault-tolerant strongly Menger ([Formula: see text]-C(A)FTSM, for short) (arc) connected if [Formula: see text] is strongly Menger (arc) connected for every [Formula: see text](respectively, [Formula: see text]) with [Formula: see text] and [Formula: see text]. The directed [Formula: see text]-ary [Formula: see text]-cube [Formula: see text] [Formula: see text] and [Formula: see text] is a digraph with vertex set [Formula: see text]. For two vertices [Formula: see text] and [Formula: see text], [Formula: see text] dominates [Formula: see text] if there exists an integer [Formula: see text], [Formula: see text], satisfying [Formula: see text]mod [Formula: see text] and [Formula: see text], when [Formula: see text]. In this paper, we show that [Formula: see text] is [Formula: see text]-arc-fault-tolerant strongly Menger arc connected for [Formula: see text], [Formula: see text]-fault-tolerant strongly Menger connected for [Formula: see text], [Formula: see text]-conditional arc-fault-tolerant strongly Menger arc connected for [Formula: see text], and [Formula: see text]-conditional fault-tolerant strongly Menger connected for [Formula: see text]. we show that [Formula: see text] [Formula: see text] is [Formula: see text]-AFTSM arc connected when [Formula: see text], [Formula: see text]-FTSM connected when [Formula: see text], [Formula: see text]-CAFTSM arc connected when [Formula: see text], and [Formula: see text]-CFTSM connected when [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219265923500123","type":"journal-article","created":{"date-parts":[[2023,7,19]],"date-time":"2023-07-19T07:34:20Z","timestamp":1689752060000},"source":"Crossref","is-referenced-by-count":1,"title":["The Strong Menger Connectivity of the Directed k-Ary n-Cube"],"prefix":"10.1142","volume":"24","author":[{"given":"Guoqiang","family":"Xie","sequence":"first","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang, 830046, P. 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