{"id":"https://openalex.org/W3010853522","doi":"https://doi.org/10.1155/2020/5608720","title":"The Property of Hamiltonian Connectedness in Toeplitz Graphs","display_name":"The Property of Hamiltonian Connectedness in Toeplitz Graphs","publication_year":2020,"publication_date":"2020-03-12","ids":{"openalex":"https://openalex.org/W3010853522","doi":"https://doi.org/10.1155/2020/5608720","mag":"3010853522"},"language":"lv","primary_location":{"id":"doi:10.1155/2020/5608720","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/5608720","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/5608720.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2020/5608720.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020468332","display_name":"Ayesha Shabbir","orcid":"https://orcid.org/0000-0002-3392-7166"},"institutions":[{"id":"https://openalex.org/I142204992","display_name":"University of Lahore","ror":"https://ror.org/051jrjw38","country_code":"PK","type":"education","lineage":["https://openalex.org/I142204992"]},{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]},{"id":"https://openalex.org/I99165933","display_name":"University of Gujrat","ror":"https://ror.org/01xe5fb92","country_code":"PK","type":"education","lineage":["https://openalex.org/I99165933"]}],"countries":["PK","SA"],"is_corresponding":false,"raw_author_name":"Ayesha Shabbir","raw_affiliation_strings":["Department of Mathematics, University of Lahore, Gujrat Campus, Gujrat, Pakistan","Preparatory Year Deanship, King Faisal University, 31982 Hofuf, Al Ahsa, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Lahore, Gujrat Campus, Gujrat, Pakistan","institution_ids":["https://openalex.org/I99165933","https://openalex.org/I142204992"]},{"raw_affiliation_string":"Preparatory Year Deanship, King Faisal University, 31982 Hofuf, Al Ahsa, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038635703","display_name":"Muhammad Faisal Nadeem","orcid":"https://orcid.org/0000-0002-3175-7191"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Faisal Nadeem","raw_affiliation_strings":["Department of Mathematics, COMSATS, University Islamabad Lahore Campus, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS, University Islamabad Lahore Campus, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050057586","display_name":"Tudor Zamfirescu","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]},{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["DE","RO"],"is_corresponding":false,"raw_author_name":"Tudor Zamfirescu","raw_affiliation_strings":["Faculty of Mathematics, University of Dortmund, 44221 Dortmund, Germany","Romanian Academy, Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Dortmund, 44221 Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Romanian Academy, Bucharest, Romania","institution_ids":["https://openalex.org/I58077936"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038635703"],"corresponding_institution_ids":["https://openalex.org/I16076960"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.7226,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.75916631,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6059372425079346},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4341597557067871},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3499821424484253}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6059372425079346},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4341597557067871},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3499821424484253}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2020/5608720","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/5608720","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/5608720.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:5608720","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2020/5608720.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:15eb3dc48e054ee4ad6e1ec60c170238","is_oa":true,"landing_page_url":"https://doaj.org/article/15eb3dc48e054ee4ad6e1ec60c170238","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2020 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2020/5608720","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/5608720","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/5608720.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G153074835","display_name":null,"funder_award_id":"186236","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3527006608","display_name":null,"funder_award_id":"2019YX002A","funder_id":"https://openalex.org/F4320322804","funder_display_name":"Deanship of Scientific Research, King Faisal University"},{"id":"https://openalex.org/G6050876609","display_name":null,"funder_award_id":"2019YX002A","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6166026595","display_name":null,"funder_award_id":"186236","funder_id":"https://openalex.org/F4320322804","funder_display_name":"Deanship of Scientific Research, King Faisal University"},{"id":"https://openalex.org/G7346218018","display_name":null,"funder_award_id":"11871","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7485055502","display_name":null,"funder_award_id":"11871192","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7837465511","display_name":null,"funder_award_id":"11871192","funder_id":"https://openalex.org/F4320322804","funder_display_name":"Deanship of Scientific Research, King Faisal University"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322804","display_name":"Deanship of Scientific Research, King Faisal University","ror":"https://ror.org/00dn43547"},{"id":"https://openalex.org/F4320331156","display_name":"King Faisal University","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3010853522.pdf","grobid_xml":"https://content.openalex.org/works/W3010853522.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W151101574","https://openalex.org/W1966678637","https://openalex.org/W1970388956","https://openalex.org/W1973860023","https://openalex.org/W1999305900","https://openalex.org/W2040271493","https://openalex.org/W2058555041","https://openalex.org/W2125292347","https://openalex.org/W2403031090","https://openalex.org/W2408593987"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W2350741829"],"abstract_inverted_index":{"A":[0,23],"spanning":[1],"path":[2],"in":[3],"a":[4,9,38],"graph":[5,24,101],"G":[6,25,34],"is":[7,19,26,52,66,108],"called":[8,27],"Hamiltonian":[10,39,92],"path.":[11,40],"To":[12],"determine":[13],"which":[14],"graphs":[15],"possess":[16],"such":[17],"paths":[18],"an":[20],"NP-complete":[21],"problem.":[22],"Hamiltonian-connected":[28,109],"if":[29],"any":[30],"two":[31],"vertices":[32],"of":[33,46,72],"are":[35],"connected":[36],"by":[37],"We":[41],"consider":[42],"here":[43],"the":[44,98],"family":[45],"Toeplitz":[47,100],"graphs.":[48],"About":[49],"them,":[50],"it":[51],"known":[53],"only":[54],"for":[55,79,110],"<mml:math":[56,60,73,80,84,102,112,116],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[57,61,74,81,85,103,113,117],"id=\"M1\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math>":[58],"that":[59,97],"id=\"M2\"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mfenced":[62],"open=\"\u2329\"":[63,76,105],"close=\"\u232a\"":[64,77,106],"separators=\"|\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math>":[65],"Hamiltonian-connected,":[67],"while":[68],"some":[69],"particular":[70],"cases":[71],"id=\"M3\"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mfenced":[75],"separators=\"|\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>,</mml:mo><mml:mi>r</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math>":[78],"id=\"M4\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>":[82],"and":[83,115],"id=\"M5\"><mml:mrow><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mn>2,3,4</mml:mn></mml:mrow></mml:math>":[86],"have":[87],"also":[88],"been":[89],"investigated":[90],"regarding":[91],"connectedness.":[93],"Here,":[94],"we":[95],"prove":[96],"nonbipartite":[99],"id=\"M6\"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mfenced":[104],"separators=\"|\"><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>,</mml:mo><mml:mi>r</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math>":[107],"all":[111],"id=\"M7\"><mml:mrow><mml:mn>1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>q</mml:mi><mml:mo>&lt;</mml:mo><mml:mi>r</mml:mi><mml:mo>&lt;</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math>":[114],"id=\"M8\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>\u2265</mml:mo><mml:mn>5</mml:mn><mml:mi>r</mml:mi><mml:mo>\u2212</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>.":[118]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
