{"id":"https://openalex.org/W3044037519","doi":"https://doi.org/10.3390/sym12081233","title":"Topological Symmetry Transition between Toroidal and Klein Bottle Graphenic Systems","display_name":"Topological Symmetry Transition between Toroidal and Klein Bottle Graphenic Systems","publication_year":2020,"publication_date":"2020-07-27","ids":{"openalex":"https://openalex.org/W3044037519","doi":"https://doi.org/10.3390/sym12081233","mag":"3044037519"},"language":"en","primary_location":{"id":"doi:10.3390/sym12081233","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081233","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1233/pdf?version=1595855977","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/8/1233/pdf?version=1595855977","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042954156","display_name":"Mihai V. Putz","orcid":"https://orcid.org/0000-0002-9781-1541"},"institutions":[{"id":"https://openalex.org/I3121153395","display_name":"West University of Timi\u015foara","ror":"https://ror.org/0583a0t97","country_code":"RO","type":"education","lineage":["https://openalex.org/I3121153395"]},{"id":"https://openalex.org/I4210130918","display_name":"National Institute of Research and Development for Electrochemistry and Condensed","ror":"https://ror.org/04egvzv93","country_code":"RO","type":"other","lineage":["https://openalex.org/I4210130918"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Mihai V. Putz","raw_affiliation_strings":["Laboratory of Renewable Energies-Photovoltaics, R&amp;D National Institute for Electrochemistry and Condensed Matter, Dr. A. Paunescu Podeanu Str. No. 144, RO-300569 Timisoara, Romania","Laboratory of Structural and Computational Physical-Chemistry for Nanosciences and QSAR, Biology-Chemistry Department, Faculty of Chemistry, Biology, Geography, West University of Timisoara, Str. Pestalozzi No. 16, 300115 Timisoara, Romania"],"raw_orcid":"https://orcid.org/0000-0002-9781-1541","affiliations":[{"raw_affiliation_string":"Laboratory of Renewable Energies-Photovoltaics, R&amp;D National Institute for Electrochemistry and Condensed Matter, Dr. A. Paunescu Podeanu Str. No. 144, RO-300569 Timisoara, Romania","institution_ids":["https://openalex.org/I4210130918"]},{"raw_affiliation_string":"Laboratory of Structural and Computational Physical-Chemistry for Nanosciences and QSAR, Biology-Chemistry Department, Faculty of Chemistry, Biology, Geography, West University of Timisoara, Str. Pestalozzi No. 16, 300115 Timisoara, Romania","institution_ids":["https://openalex.org/I3121153395"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002712424","display_name":"Ottorino Ori","orcid":"https://orcid.org/0000-0002-0842-2684"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ottorino Ori","raw_affiliation_strings":["Actinium Chemical Research Institute, Via Casilina 1626/A, 00133 Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0002-0842-2684","affiliations":[{"raw_affiliation_string":"Actinium Chemical Research Institute, Via Casilina 1626/A, 00133 Rome, Italy","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002712424","https://openalex.org/A5042954156"],"corresponding_institution_ids":["https://openalex.org/I3121153395","https://openalex.org/I4210130918"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.4685,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.81840588,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"12","issue":"8","first_page":"1233","last_page":"1233"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10956","display_name":"Fullerene Chemistry and Applications","score":0.9747999906539917,"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/klein-bottle","display_name":"Klein bottle","score":0.8790799975395203},{"id":"https://openalex.org/keywords/wiener-index","display_name":"Wiener index","score":0.6306291222572327},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5314211845397949},{"id":"https://openalex.org/keywords/zigzag","display_name":"Zigzag","score":0.49033379554748535},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.420604944229126},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.37415581941604614},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3655000329017639},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.3599874973297119},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21967345476150513},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2130853235721588}],"concepts":[{"id":"https://openalex.org/C192349906","wikidata":"https://www.wikidata.org/wiki/Q23638","display_name":"Klein bottle","level":3,"score":0.8790799975395203},{"id":"https://openalex.org/C16640446","wikidata":"https://www.wikidata.org/wiki/Q909065","display_name":"Wiener index","level":3,"score":0.6306291222572327},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5314211845397949},{"id":"https://openalex.org/C192271897","wikidata":"https://www.wikidata.org/wiki/Q198438","display_name":"Zigzag","level":2,"score":0.49033379554748535},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.420604944229126},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37415581941604614},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3655000329017639},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.3599874973297119},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21967345476150513},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2130853235721588}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12081233","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081233","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1233/pdf?version=1595855977","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:68b634b3e0c24b70a8fd5f82ad66a9ce","is_oa":true,"landing_page_url":"https://doaj.org/article/68b634b3e0c24b70a8fd5f82ad66a9ce","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":"Symmetry, Vol 12, Iss 8, p 1233 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/8/1233/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12081233","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12081233","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081233","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1233/pdf?version=1595855977","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3044037519.pdf","grobid_xml":"https://content.openalex.org/works/W3044037519.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W11476871","https://openalex.org/W342440327","https://openalex.org/W1964189680","https://openalex.org/W1965201816","https://openalex.org/W1975235647","https://openalex.org/W1980702681","https://openalex.org/W1981125802","https://openalex.org/W1981583743","https://openalex.org/W1983536178","https://openalex.org/W1984632158","https://openalex.org/W1984946621","https://openalex.org/W1998507910","https://openalex.org/W1999911088","https://openalex.org/W2002319008","https://openalex.org/W2014935324","https://openalex.org/W2018858346","https://openalex.org/W2030695658","https://openalex.org/W2036572909","https://openalex.org/W2039188986","https://openalex.org/W2039681658","https://openalex.org/W2046941683","https://openalex.org/W2050605560","https://openalex.org/W2054701681","https://openalex.org/W2055993996","https://openalex.org/W2058122340","https://openalex.org/W2059363846","https://openalex.org/W2061069100","https://openalex.org/W2074043564","https://openalex.org/W2079372218","https://openalex.org/W2086848380","https://openalex.org/W2088784695","https://openalex.org/W2094366212","https://openalex.org/W2138371284","https://openalex.org/W2161316267","https://openalex.org/W2171414583","https://openalex.org/W2171443027","https://openalex.org/W2315497698","https://openalex.org/W2327747454","https://openalex.org/W2478461807","https://openalex.org/W2482803778","https://openalex.org/W2486362504","https://openalex.org/W2495205774","https://openalex.org/W2564973405","https://openalex.org/W2728819013","https://openalex.org/W2748839528","https://openalex.org/W2783320616","https://openalex.org/W2947172408","https://openalex.org/W2954097595","https://openalex.org/W3003939530","https://openalex.org/W3099018298","https://openalex.org/W3099048307","https://openalex.org/W3103034048","https://openalex.org/W4231210918","https://openalex.org/W4242913879","https://openalex.org/W4246319132","https://openalex.org/W4388376981","https://openalex.org/W6681806032","https://openalex.org/W6730725877","https://openalex.org/W6986865047"],"related_works":["https://openalex.org/W2786725402","https://openalex.org/W2329851968","https://openalex.org/W2041527876","https://openalex.org/W4210625684","https://openalex.org/W3087868383","https://openalex.org/W4299805552","https://openalex.org/W2755801538","https://openalex.org/W3104321287","https://openalex.org/W585882673","https://openalex.org/W2883356504"],"abstract_inverted_index":{"In":[0],"the":[1,8,12,33,50,54,68,88,103,107,132,138,143,147,168,186,204,208,240,254,262,271],"current":[2],"study,":[3],"distance-based":[4],"topological":[5,13,108,118,129,201,242,256],"invariants,":[6],"namely":[7],"Wiener":[9],"number":[10],"and":[11,21,26,43,114,207],"roundness":[14],"index,":[15],"were":[16],"computed":[17],"for":[18,193],"graphenic":[19,144,217,243],"tori":[20,145],"Klein":[22,27,77,148,172,194],"bottles":[23],"(named":[24],"toroidal":[25,85],"bottle":[28,78,149,173,195],"fullerenes":[29,174],"or":[30],"polyhexes":[31,150],"in":[32],"pre-graphene":[34],"literature)":[35],"described":[36],"as":[37,277],"closed":[38],"graphs":[39,80,136,158,197],"with":[40,46,87,151,227,270],"N":[41,47],"vertices":[42],"3N/2":[44],"edges,":[45],"depending":[48],"on":[49,167],"variable":[51],"length":[52,65],"of":[53,58,67,106,135,142,170,212,216,261,274,286],"cylindrical":[55],"edge":[56],"LC":[57,153],"these":[59,157,171,213],"nano-structures,":[60],"which":[61],"have":[62],"a":[63,95,164,199],"constant":[64],"LM":[66],"M\u00f6bius":[69],"zigzag":[70],"edge.":[71],"The":[72,219],"presented":[73],"results":[74],"show":[75],"that":[76,110,120,163,231],"cubic":[79,196],"are":[81],"topologically":[82],"indistinguishable":[83],"from":[84,239],"lattices":[86],"same":[89,104],"size":[90,98,152],"(N,":[91],"LC,":[92,155],"LM)":[93],"over":[94],"certain":[96],"threshold":[97],"LC.":[99],"Both":[100],"nano-structures":[101],"share":[102],"values":[105],"indices":[109],"measure":[111],"graph":[112],"compactness":[113],"roundness,":[115],"two":[116,133,214],"key":[117],"properties":[119,206],"largely":[121],"influence":[122],"lattice":[123],"stability.":[124],"Moreover,":[125],"this":[126],"newly":[127],"conjectured":[128],"similarity":[130],"between":[131],"kinds":[134],"transfers":[137],"translation":[139],"invariance":[140],"typical":[141],"to":[146,179,253,267],"\u2265":[154],"making":[156],"vertex":[159],"transitive.":[160],"This":[161,189],"means":[162],"traveler":[165],"jumping":[166],"nodes":[169],"is":[175,235,278],"no":[176],"longer":[177],"able":[178],"distinguish":[180],"among":[181],"them":[182],"by":[183,282],"only":[184],"measuring":[185],"chemical":[187,210],"distances.":[188],"size-induced":[190],"symmetry":[191],"transition":[192],"represents":[198],"relevant":[200],"effect":[202],"influencing":[203],"electronic":[205],"theoretical":[209],"stability":[211],"families":[215],"nano-systems.":[218],"present":[220],"finding,":[221],"nonetheless,":[222],"provides":[223],"an":[224],"original":[225],"argument,":[226],"potential":[228],"future":[229],"applications,":[230],"physical":[232],"unification":[233,257,285],"theory":[234],"possible,":[236],"starting":[237],"surprisingly":[238],"nano-chemical":[241],"space;":[244],"thus,":[245],"speculative":[246],"hypotheses":[247],"may":[248],"be":[249],"drawn,":[250],"particularly":[251],"relating":[252],"computational":[255],"(that":[258],"is,":[259],"complexification)":[260],"quantum":[263],"many-worlds":[264],"picture":[265],"(according":[266],"Everett\u2019s":[268],"theory)":[269],"space-curvature":[272],"sphericity/roundness":[273],"general":[275],"relativity,":[276],"also":[279],"currently":[280],"advocated":[281],"Wolfram\u2019s":[283],"language":[284],"matter-physical":[287],"phenomenology.":[288]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
