{"id":"https://openalex.org/W2810124054","doi":"https://doi.org/10.3390/sym10070244","title":"Computing Zagreb Indices and Zagreb Polynomials for Symmetrical Nanotubes","display_name":"Computing Zagreb Indices and Zagreb Polynomials for Symmetrical Nanotubes","publication_year":2018,"publication_date":"2018-06-28","ids":{"openalex":"https://openalex.org/W2810124054","doi":"https://doi.org/10.3390/sym10070244","mag":"2810124054"},"language":"en","primary_location":{"id":"doi:10.3390/sym10070244","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10070244","pdf_url":"https://www.mdpi.com/2073-8994/10/7/244/pdf?version=1530179679","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/2073-8994/10/7/244/pdf?version=1530179679","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012636371","display_name":"Zehui Shao","orcid":"https://orcid.org/0000-0003-0764-4135"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zehui Shao","raw_affiliation_strings":["Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China"],"raw_orcid":"https://orcid.org/0000-0003-0764-4135","affiliations":[{"raw_affiliation_string":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032531659","display_name":"Muhammad Kamran Siddiqui","orcid":"https://orcid.org/0000-0002-2607-4847"},"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 Kamran Siddiqui","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Sahiwal 57000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-2607-4847","affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Sahiwal 57000, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082218567","display_name":"Mehwish Hussain Muhammad","orcid":"https://orcid.org/0000-0003-4879-1588"},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mehwish Hussain Muhammad","raw_affiliation_strings":["College of Chemistry and Molecular Engineering, Zhengzhou University, Zhengzhou 450001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Chemistry and Molecular Engineering, Zhengzhou University, Zhengzhou 450001, China","institution_ids":["https://openalex.org/I38877650"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5032531659"],"corresponding_institution_ids":["https://openalex.org/I16076960"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":23.452,"has_fulltext":true,"cited_by_count":128,"citation_normalized_percentile":{"value":0.99845817,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"10","issue":"7","first_page":"244","last_page":"244"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10211","display_name":"Computational Drug Discovery Methods","score":0.9921000003814697,"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/T11298","display_name":"Synthesis and Properties of Aromatic Compounds","score":0.9919000267982483,"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/topological-index","display_name":"Topological index","score":0.7469634413719177},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6383030414581299},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49560534954071045},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4948222041130066},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47550731897354126},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4692763090133667},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.43651625514030457},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4338158369064331},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3627518117427826},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28037598729133606}],"concepts":[{"id":"https://openalex.org/C159867001","wikidata":"https://www.wikidata.org/wiki/Q904942","display_name":"Topological index","level":2,"score":0.7469634413719177},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6383030414581299},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49560534954071045},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4948222041130066},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47550731897354126},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4692763090133667},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.43651625514030457},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4338158369064331},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3627518117427826},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28037598729133606},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym10070244","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10070244","pdf_url":"https://www.mdpi.com/2073-8994/10/7/244/pdf?version=1530179679","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:063ad7d94e4a43b4b8d9658810209083","is_oa":true,"landing_page_url":"https://doaj.org/article/063ad7d94e4a43b4b8d9658810209083","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 10, Iss 7, p 244 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym10070244","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10070244","pdf_url":"https://www.mdpi.com/2073-8994/10/7/244/pdf?version=1530179679","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/W2810124054.pdf","grobid_xml":"https://content.openalex.org/works/W2810124054.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W74903757","https://openalex.org/W1755416306","https://openalex.org/W1794818888","https://openalex.org/W1979281101","https://openalex.org/W2013283019","https://openalex.org/W2021163909","https://openalex.org/W2029713676","https://openalex.org/W2065534534","https://openalex.org/W2109460231","https://openalex.org/W2186144882","https://openalex.org/W2252948910","https://openalex.org/W2257817890","https://openalex.org/W2316867176","https://openalex.org/W2318794083","https://openalex.org/W2344803877","https://openalex.org/W2528508285","https://openalex.org/W2618563307","https://openalex.org/W2619493822","https://openalex.org/W2743718144","https://openalex.org/W2749104725","https://openalex.org/W2751765604","https://openalex.org/W2754496428","https://openalex.org/W2802461145","https://openalex.org/W2803831121","https://openalex.org/W3178029460","https://openalex.org/W6638401968","https://openalex.org/W6676651168","https://openalex.org/W6686704686","https://openalex.org/W6691665271","https://openalex.org/W6744075481","https://openalex.org/W6798427763"],"related_works":["https://openalex.org/W4293583306","https://openalex.org/W2798504042","https://openalex.org/W4366550101","https://openalex.org/W2466559673","https://openalex.org/W2901172912","https://openalex.org/W3175357564","https://openalex.org/W2979113253","https://openalex.org/W2337950557","https://openalex.org/W2345961532","https://openalex.org/W2473959779"],"abstract_inverted_index":{"Topological":[0],"indices":[1,15,36,50,73],"are":[2,51],"numbers":[3],"related":[4],"to":[5,8,17],"sub-atomic":[6],"graphs":[7],"allow":[9],"quantitative":[10],"structure-movement/property/danger":[11],"connections.":[12],"These":[13,49],"topological":[14,35],"correspond":[16],"some":[18],"specific":[19,60],"physico-concoction":[20],"properties":[21],"such":[22],"as":[23],"breaking":[24],"point,":[25],"security,":[26],"strain":[27],"vitality":[28],"of":[29,34,46,56,59,72],"chemical":[30],"compounds.":[31],"The":[32],"idea":[33],"were":[37],"set":[38],"up":[39],"in":[40,44,53],"compound":[41,63],"graph":[42],"hypothesis":[43],"view":[45],"vertex":[47],"degrees.":[48],"valuable":[52],"the":[54],"investigation":[55],"mitigating":[57],"exercises":[58],"Nanotubes":[61,80],"and":[62,74],"systems.":[64],"In":[65],"this":[66],"paper,":[67],"we":[68],"discuss":[69],"Zagreb":[70,75],"types":[71],"polynomials":[76],"for":[77],"a":[78],"few":[79],"covered":[81],"by":[82],"cycles.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":30},{"year":2021,"cited_by_count":27},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":9}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}