{"id":"https://openalex.org/W4214524324","doi":"https://doi.org/10.1142/s0129054122500058","title":"Extra Connectivity and Structure Connectivity of 2-Dimensional Torus Networks","display_name":"Extra Connectivity and Structure Connectivity of 2-Dimensional Torus Networks","publication_year":2022,"publication_date":"2022-02-01","ids":{"openalex":"https://openalex.org/W4214524324","doi":"https://doi.org/10.1142/s0129054122500058"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054122500058","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054122500058","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090047899","display_name":"Dongqin Cheng","orcid":"https://orcid.org/0000-0001-9933-6601"},"institutions":[{"id":"https://openalex.org/I159948400","display_name":"Jinan University","ror":"https://ror.org/02xe5ns62","country_code":"CN","type":"education","lineage":["https://openalex.org/I159948400"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dongqin Cheng","raw_affiliation_strings":["Department of Mathematics, College of Information Science and Technology, Jinan University, 510632, Guangzhou, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Information Science and Technology, Jinan University, 510632, Guangzhou, P. R. China","institution_ids":["https://openalex.org/I159948400"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090047899"],"corresponding_institution_ids":["https://openalex.org/I159948400"],"apc_list":null,"apc_paid":null,"fwci":1.1414,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.78397154,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"33","issue":"02","first_page":"155","last_page":"173"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10083","display_name":"Graphene research and applications","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10074","display_name":"Carbon Nanotubes in Composites","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.7641284465789795},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5252805948257446},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.44893771409988403},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4399181604385376},{"id":"https://openalex.org/keywords/substructure","display_name":"Substructure","score":0.4326581358909607},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.326479434967041},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31232741475105286},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11123639345169067}],"concepts":[{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.7641284465789795},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5252805948257446},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.44893771409988403},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4399181604385376},{"id":"https://openalex.org/C99679407","wikidata":"https://www.wikidata.org/wiki/Q56761637","display_name":"Substructure","level":2,"score":0.4326581358909607},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.326479434967041},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31232741475105286},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11123639345169067},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054122500058","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054122500058","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W159485782","https://openalex.org/W560799365","https://openalex.org/W1971967319","https://openalex.org/W1973369737","https://openalex.org/W2066502816","https://openalex.org/W2122056736","https://openalex.org/W2124839136","https://openalex.org/W2126385009","https://openalex.org/W2165021839","https://openalex.org/W2209020398","https://openalex.org/W2209962516","https://openalex.org/W2338928843","https://openalex.org/W2523017701","https://openalex.org/W2570964266","https://openalex.org/W2600917856","https://openalex.org/W2741570370","https://openalex.org/W2765797550","https://openalex.org/W2773181532","https://openalex.org/W2777090724","https://openalex.org/W2780334646","https://openalex.org/W2792939965","https://openalex.org/W2809437418","https://openalex.org/W2904776587","https://openalex.org/W2912246636","https://openalex.org/W2914354594","https://openalex.org/W2963538553","https://openalex.org/W2964124349","https://openalex.org/W2967859923","https://openalex.org/W2970021913","https://openalex.org/W2972312980","https://openalex.org/W2982162357","https://openalex.org/W3017395036","https://openalex.org/W3025783708","https://openalex.org/W3026315868","https://openalex.org/W3084238996","https://openalex.org/W3084558384","https://openalex.org/W3118844787","https://openalex.org/W3157623146","https://openalex.org/W3214564065","https://openalex.org/W4237486254","https://openalex.org/W4241831968","https://openalex.org/W4253941973"],"related_works":["https://openalex.org/W3153444835","https://openalex.org/W2153916713","https://openalex.org/W2023846184","https://openalex.org/W2703419385","https://openalex.org/W2329056228","https://openalex.org/W2284584236","https://openalex.org/W1979083399","https://openalex.org/W2374530195","https://openalex.org/W2953357932","https://openalex.org/W2043946748"],"abstract_inverted_index":{"The":[0,21],"2-dimensional":[1,84],"torus":[2,19,85],"networks,":[3],"denoted":[4],"by":[5],"[Formula:":[6,16,48,52,56,63,67,74,79,87,94,101,105,109,120],"see":[7,17,49,53,57,64,68,75,80,88,91,95,102,106,110,121,124],"text],":[8,103],"is":[9,126],"a":[10],"special":[11],"case":[12],"of":[13,36,47,62,83,119],"the":[14,34,37,44,73,98,117],"famous":[15],"text]-dimensional":[18],"network.":[20],"extra":[22],"connectivity,":[23],"structure":[24,99],"connectivity":[25,28,31,46,61,77,82,118],"and":[26,55,59,78,93,108],"sub-structure":[27],"are":[29,114],"generalized":[30],"to":[32],"measure":[33],"fault-tolerance":[35],"networks.":[38],"In":[39],"this":[40],"paper,":[41],"we":[42],"show":[43],"1-extra":[45],"text]":[50,54,58,65,89,92,107,122],"for":[51,66],"2-extra":[60],"text].":[69,111],"We":[70],"also":[71],"determine":[72],"text]-structure":[76],"text]-substructure":[81],"network":[86],"([Formula:":[90,123],"text])":[96,125],"when":[97],"subgraph":[100],"where":[104],"These":[112],"results":[113],"sharp":[115],"since":[116],"4.":[127]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-25T08:17:42.794288","created_date":"2025-10-10T00:00:00"}
