{"id":"https://openalex.org/W7213598097","doi":"https://doi.org/10.48550/arxiv.2609.19766","title":"The resonance graphs of nanotubes and toroidal polyhexes","display_name":"The resonance graphs of nanotubes and toroidal polyhexes","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213598097","doi":"https://doi.org/10.48550/arxiv.2609.19766"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.19766","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19766","pdf_url":"https://arxiv.org/pdf/2609.19766","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.19766","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010936786","display_name":"Lingmei Liang","orcid":null,"observed_orcids":[]},"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":"Liang, Lingmei","raw_affiliation_strings":["School of Mathematics and Statistics , Lanzhou University , Lanzhou , Gansu 730000 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Lanzhou University , Lanzhou , Gansu 730000 , P. R. China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5152121339","display_name":"Heping Zhang","orcid":null,"observed_orcids":[]},"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":"Zhang, Heping","raw_affiliation_strings":["School of Mathematics and Statistics , Lanzhou University , Lanzhou , Gansu 730000 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Lanzhou University , Lanzhou , Gansu 730000 , P. R. China","institution_ids":["https://openalex.org/I76214153"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I76214153"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.0007999999797903001,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nanotubes","display_name":"nanotubes","score":0.9309999942779541},{"id":"https://openalex.org/keywords/c60","display_name":"C60","score":0.7770000100135803},{"id":"https://openalex.org/keywords/perfect-matchings","display_name":"perfect matchings","score":0.824999988079071},{"id":"https://openalex.org/keywords/carbon-networks","display_name":"carbon networks","score":0.6610000133514404},{"id":"https://openalex.org/keywords/ladders","display_name":"ladders","score":0.675000011920929},{"id":"https://openalex.org/keywords/torus","display_name":"torus","score":0.5590000152587891},{"id":"https://openalex.org/keywords/connected-components","display_name":"connected components","score":0.6430000066757202}],"concepts":[{"id":"https://openalex.org/C15001198","wikidata":"https://www.wikidata.org/wiki/Q3241394","display_name":"Toroid","level":3,"score":0.8184000253677368},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.6101999878883362},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5138999819755554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47380000352859497},{"id":"https://openalex.org/C513720949","wikidata":"https://www.wikidata.org/wiki/Q1778729","display_name":"Carbon nanotube","level":2,"score":0.45719999074935913},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.44359999895095825},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.4375},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.41519999504089355},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.36880001425743103},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.3091000020503998},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.2971999943256378},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2939999997615814},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26579999923706055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.19766","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19766","pdf_url":"https://arxiv.org/pdf/2609.19766","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.19766","doi":"https://doi.org/10.48550/arxiv.2609.19766","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.19766","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.19766","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19766","pdf_url":"https://arxiv.org/pdf/2609.19766","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6714676085","display_name":null,"funder_award_id":"12671409","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8173501753","display_name":null,"funder_award_id":"12271229","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213598097.pdf","grobid_xml":"https://content.openalex.org/works/W7213598097.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7203665815","https://openalex.org/W2300238937","https://openalex.org/W1968971602","https://openalex.org/W7050438345","https://openalex.org/W7024130065","https://openalex.org/W4400590339","https://openalex.org/W2182749664","https://openalex.org/W9591846","https://openalex.org/W2053217301","https://openalex.org/W4387941816"],"abstract_inverted_index":{"Coronoid":[0],"systems,":[1],"nanotubes":[2,30,82],"and":[3,29,38,83,130,132,150],"toroidal":[4,84,105,137],"polyhexes":[5],"(or":[6],"fullerenes)":[7],"can":[8,154],"all":[9],"be":[10,155],"regarded":[11],"as":[12],"carbon":[13,17],"networks":[14],"composed":[15],"of":[16,26,61,74,101,114,144],"atoms":[18],"linked":[19],"in":[20,56,109,165],"hexagonal":[21],"shapes.":[22],"The":[23],"resonance":[24,63,116],"graphs":[25],"coronoid":[27,36],"systems":[28,37],"are":[31],"not":[32,78],"necessarily":[33],"connected.":[34],"For":[35,136],"elementary":[39],"nanotubes,":[40],"by":[41,157],"using":[42,158],"flow":[43],"across":[44,123],"cuts":[45,124],"the":[46,57,62,72,110,120,126,133,148,151,163],"present":[47],"authors":[48],"gave":[49],"criteria":[50,96],"for":[51,80,97,162],"two":[52,98,167],"perfect":[53,99,168],"matchings":[54,100,169],"lying":[55],"same":[58,111,121,134],"connected":[59,112],"component":[60,113],"graph":[64],"(Discrete":[65],"Appl.":[66],"Math.":[67],"395":[68],"(2026)":[69],"443-455).":[70],"However,":[71],"sufficiency":[73],"such":[75],"criterion":[76,153],"does":[77],"hold":[79],"general":[81],"polyhexes.":[85],"In":[86],"this":[87,91],"paper":[88],"we":[89],"strengthen":[90],"requirement":[92],"to":[93,107],"obtain":[94],"valid":[95],"a":[102],"nanotube":[103],"(resp.":[104,128],"polyhex)":[106],"lie":[108],"its":[115],"graph:":[117],"they":[118],"have":[119,170],"flows":[122],"along":[125],"$x$-axis":[127],"longitude":[129],"latitude)":[131],"ladders.":[135],"polyhexes,":[138],"our":[139],"method":[140],"uses":[141],"homotopic":[142],"classes":[143],"simple":[145,160],"loops":[146],"on":[147],"torus,":[149],"above":[152],"simplified":[156],"only":[159],"flows,":[161],"case":[164],"which":[166],"alternating":[171],"hexagons.":[172]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-19T00:00:00"}
