{"id":"https://openalex.org/W2101199563","doi":"https://doi.org/10.1155/2014/196792","title":"Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces","display_name":"Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2101199563","doi":"https://doi.org/10.1155/2014/196792","mag":"2101199563"},"language":"lv","primary_location":{"id":"doi:10.1155/2014/196792","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/196792","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/196792.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","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/jam/2014/196792.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103158171","display_name":"Yang Gao","orcid":"https://orcid.org/0000-0002-5690-7408"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Gao","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China"],"raw_orcid":"https://orcid.org/0000-0002-5690-7408","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056609757","display_name":"Heping Zhang","orcid":"https://orcid.org/0000-0001-5385-6687"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Heping Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China","institution_ids":["https://openalex.org/I76214153"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056609757"],"corresponding_institution_ids":["https://openalex.org/I76214153"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.3206,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.61569485,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10956","display_name":"Fullerene Chemistry and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10956","display_name":"Fullerene Chemistry and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10083","display_name":"Graphene research and applications","score":0.9994999766349792,"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/T11298","display_name":"Synthesis and Properties of Aromatic Compounds","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4219816327095032},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.33883199095726013},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.325142502784729},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2570689022541046}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4219816327095032},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.33883199095726013},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.325142502784729},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2570689022541046}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1155/2014/196792","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/196792","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/196792.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/118940","is_oa":true,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/118940","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1425305946","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1425305946","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:196792","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/196792.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:709ae3b3950a4fceb6460986d062b54c","is_oa":true,"landing_page_url":"https://doaj.org/article/709ae3b3950a4fceb6460986d062b54c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/196792","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/196792","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/196792.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2561142962","display_name":null,"funder_award_id":"lzujbky-2014-21","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3656695710","display_name":null,"funder_award_id":"11371180","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G6490518970","display_name":null,"funder_award_id":"lzujbky-2014-21","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G8462370252","display_name":"\u56fe\u7684\u5339\u914d\u5f3a\u8feb\u4e0e\u5339\u914d\u963b\u788d\u95ee\u9898\u7814\u7a76","funder_award_id":"11371180","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2101199563.pdf","grobid_xml":"https://content.openalex.org/works/W2101199563.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1468959","https://openalex.org/W247697463","https://openalex.org/W606471319","https://openalex.org/W1578352082","https://openalex.org/W1602998205","https://openalex.org/W1977338558","https://openalex.org/W1984946621","https://openalex.org/W1990879687","https://openalex.org/W1993844040","https://openalex.org/W1995632106","https://openalex.org/W1996101707","https://openalex.org/W2005339375","https://openalex.org/W2011994372","https://openalex.org/W2039563014","https://openalex.org/W2047451085","https://openalex.org/W2049568114","https://openalex.org/W2059032189","https://openalex.org/W2072317569","https://openalex.org/W2076423910","https://openalex.org/W2092872267","https://openalex.org/W2121442810","https://openalex.org/W2144254936","https://openalex.org/W2146809387","https://openalex.org/W2157425599","https://openalex.org/W2165594803","https://openalex.org/W2202363117","https://openalex.org/W2338830639","https://openalex.org/W3162055135","https://openalex.org/W4234586542"],"related_works":["https://openalex.org/W4246450666","https://openalex.org/W4388998267","https://openalex.org/W2898370298","https://openalex.org/W4390401159","https://openalex.org/W2744391499","https://openalex.org/W3120461830","https://openalex.org/W4230250635","https://openalex.org/W3041790586","https://openalex.org/W2018879842","https://openalex.org/W3144504424"],"abstract_inverted_index":{"Fowler":[0],"and":[1,22,83,152],"Pisanski":[2],"showed":[3,39],"that":[4,40],"the":[5,30,41,70,80,84,88,92,95,155,173,176],"Fries":[6,137],"number":[7,43,122,138],"for":[8,69,114],"a":[9,45,77,115],"fullerene":[10,46],"on":[11,35,47,87,94,117,157,175],"surface":[12,36,48,118,158],"\u03a3":[13,49,159],"is":[14,50,123,139],"bounded":[15,51,124,140],"above":[16,52,125,141],"by<mml:math":[17,53,126,142],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[18,54,64,97,103,127,143,179,185],"id=\"M1\"><mml:mo":[19],"stretchy=\"false\">|</mml:mo><mml:mi>V</mml:mi><mml:mo":[20,57,106,130,146,188],"stretchy=\"false\">|</mml:mo><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:math>,":[21],"fullerenes":[23,34,82,93,174],"which":[24,99,181],"attain":[25],"this":[26],"bound":[27],"are":[28],"exactly":[29],"class":[31],"of":[32,44,73,166],"leapfrog":[33],"\u03a3.":[37,74],"We":[38,111],"Clar":[42,100,121,168,182],"id=\"M2\"><mml:mo":[55],"stretchy=\"false\">(</mml:mo><mml:mo":[56,105,129,145,187],"stretchy=\"false\">|</mml:mo><mml:mo>/</mml:mo><mml:mn>6</mml:mn><mml:mo":[58,107,131,189],"stretchy=\"false\">)</mml:mo><mml:mo>-</mml:mo><mml:mi>\u03c7</mml:mi><mml:mo":[59,108,190],"stretchy=\"false\">(</mml:mo><mml:mi":[60,66,133,149],"mathvariant=\"normal\">\u03a3</mml:mi><mml:mo":[61,67,134,150],"stretchy=\"false\">)</mml:mo></mml:math>,":[62,151],"where<mml:math":[63],"id=\"M3\"><mml:mi>\u03c7</mml:mi><mml:mo":[65],"stretchy=\"false\">)</mml:mo></mml:math>stands":[68],"Euler":[71],"characteristic":[72],"By":[75],"establishing":[76],"relation":[78],"between":[79],"extremal":[81,85],"(4,6)-fullerenes":[86,156],"sphere,":[89],"Hartung":[90],"characterized":[91],"sphere<mml:math":[96],"id=\"M4\"><mml:mrow><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>for":[98],"numbers":[101,183],"attain<mml:math":[102,184],"id=\"M5\"><mml:mo":[104],"stretchy=\"false\">(</mml:mo><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo":[109],"stretchy=\"false\">)</mml:mo></mml:math>.":[110],"prove":[112],"that,":[113],"(4,6)-fullerene":[116],"\u03a3,":[119],"its":[120,136],"id=\"M6\"><mml:mo":[128],"stretchy=\"false\">)</mml:mo><mml:mo>+</mml:mo><mml:mi>\u03c7</mml:mi><mml:mo":[132,148],"stretchy=\"false\">)</mml:mo></mml:math>and":[135],"id=\"M7\"><mml:mo":[144],"stretchy=\"false\">|</mml:mo><mml:mo>/</mml:mo><mml:mn>3</mml:mn><mml:mo":[147],"we":[153,171],"characterize":[154,172],"attaining":[160],"these":[161],"two":[162],"bounds":[163],"in":[164],"terms":[165],"perfect":[167],"structure.":[169],"Moreover,":[170],"projective":[177],"plane<mml:math":[178],"id=\"M8\"><mml:mrow><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>for":[180],"id=\"M9\"><mml:mo":[186],"stretchy=\"false\">(</mml:mo><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo":[191],"stretchy=\"false\">)</mml:mo></mml:math>in":[192],"Hartung\u2019s":[193],"method.":[194]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}