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We also determine the [Formula: see text]-structure connectivity and [Formula: see text]-substructure connectivity of 2-dimensional torus network [Formula: see text] ([Formula: see text] and [Formula: see text]) when the structure subgraph [Formula: see text], where [Formula: see text] and [Formula: see text]. These results are sharp since the connectivity of [Formula: see text] ([Formula: see text]) is 4.<\/jats:p>","DOI":"10.1142\/s0129054122500058","type":"journal-article","created":{"date-parts":[[2022,3,1]],"date-time":"2022-03-01T01:28:29Z","timestamp":1646098109000},"page":"155-173","source":"Crossref","is-referenced-by-count":10,"title":["Extra Connectivity and Structure Connectivity of 2-Dimensional Torus Networks"],"prefix":"10.1142","volume":"33","author":[{"given":"Dongqin","family":"Cheng","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Information Science and Technology, Jinan University, 510632, Guangzhou, P. R. 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