{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:09:32Z","timestamp":1753884572867,"version":"3.41.2"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301217"],"award-info":[{"award-number":["11301217"]}],"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":[[2022,3]]},"abstract":"<jats:p> An interconnection network is usually modeled by a connected graph in which vertices represent processors and edges represent links between processors. The connectivity is an important parameter to evaluate the fault tolerance of interconnection networks. A connected graph [Formula: see text] is maximally local-(edge-)connected if each pair vertices [Formula: see text] of [Formula: see text] is connected by min[Formula: see text] pairwise (edge-)disjoint paths between [Formula: see text] and [Formula: see text] in [Formula: see text]. A graph [Formula: see text] is called [Formula: see text]-fault-tolerant maximally local-(edge-)connected if [Formula: see text] is maximally local-(edge-)connected for any [Formula: see text] ([Formula: see text]) with [Formula: see text]. A graph [Formula: see text] is called [Formula: see text]-fault-tolerant maximally local-(edge-)connected of order [Formula: see text] if [Formula: see text] is maximally local-(edge-)connected for any [Formula: see text] with [Formula: see text], where [Formula: see text] is a conditional faulty vertex (edge) set of order [Formula: see text]. In this paper, we obtain the sufficient condition of connected graphs to be [Formula: see text]-edge-fault-tolerant maximally local-edge-connected. Moreover, we consider the sufficient condition of connected graphs to be [Formula: see text]-fault-tolerant maximally local-(edge-)connected of order [Formula: see text]. Some previous results in [Theor. Comput. Sci.\u00a0731 (2018) 50\u201367] and [Theor. Comput. Sci.\u00a0847 (2020) 39\u201348] are extended. <\/jats:p>","DOI":"10.1142\/s0219265921420184","type":"journal-article","created":{"date-parts":[[2022,2,25]],"date-time":"2022-02-25T03:01:17Z","timestamp":1645758077000},"source":"Crossref","is-referenced-by-count":0,"title":["The Sufficient Conditions of (\u03b4(G) \u2212 2)-(|F|-)Fault-Tolerant Maximal Local-(Edge-)Connectivity of Connected Graphs"],"prefix":"10.1142","volume":"22","author":[{"given":"Shanshan","family":"Yin","sequence":"first","affiliation":[{"name":"School of Science, Jimei University, Xiamen, Fujian 361021, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2060-9289","authenticated-orcid":false,"given":"Liqiong","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Science, Jimei University, Xiamen, Fujian 361021, P. R. China"}]},{"given":"Weihua","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, P. R. 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