{"id":"https://openalex.org/W2900385113","doi":"https://doi.org/10.1142/s1793830919500022","title":"Molecular trees with the sixth, seventh and eighth minimal irregularity values","display_name":"Molecular trees with the sixth, seventh and eighth minimal irregularity values","publication_year":2018,"publication_date":"2018-11-08","ids":{"openalex":"https://openalex.org/W2900385113","doi":"https://doi.org/10.1142/s1793830919500022","mag":"2900385113"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830919500022","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830919500022","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005713893","display_name":"\u0410\u043b\u0438 \u0420\u0435\u0437\u0430 \u0410\u0448\u0440\u0430\u0444\u0438","orcid":"https://orcid.org/0000-0002-2858-0663"},"institutions":[{"id":"https://openalex.org/I105818395","display_name":"University of Kashan","ror":"https://ror.org/015zmr509","country_code":"IR","type":"education","lineage":["https://openalex.org/I105818395"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Ali Reza Ashrafi","raw_affiliation_strings":["Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317\u201353153, I R Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317\u201353153, I R Iran","institution_ids":["https://openalex.org/I105818395"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030638948","display_name":"Ali Ghalavand","orcid":null},"institutions":[{"id":"https://openalex.org/I105818395","display_name":"University of Kashan","ror":"https://ror.org/015zmr509","country_code":"IR","type":"education","lineage":["https://openalex.org/I105818395"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ali Ghalavand","raw_affiliation_strings":["Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317\u201353153, I R Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317\u201353153, I R Iran","institution_ids":["https://openalex.org/I105818395"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046231788","display_name":"Akbar Ali","orcid":"https://orcid.org/0000-0001-8160-4196"},"institutions":[{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Akbar Ali","raw_affiliation_strings":["Knowledge Unit of Science, University of Management and Technology, Sialkot 51310, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-8160-4196","affiliations":[{"raw_affiliation_string":"Knowledge Unit of Science, University of Management and Technology, Sialkot 51310, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005713893"],"corresponding_institution_ids":["https://openalex.org/I105818395"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.21731908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"11","issue":"01","first_page":"1950002","last_page":"1950002"},"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/T11298","display_name":"Synthesis and Properties of Aromatic Compounds","score":0.9951000213623047,"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/T10211","display_name":"Computational Drug Discovery Methods","score":0.9937999844551086,"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/combinatorics","display_name":"Combinatorics","score":0.7422260046005249},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7337064146995544},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.562377393245697},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4683738648891449}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7422260046005249},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7337064146995544},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.562377393245697},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4683738648891449}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830919500022","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830919500022","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G734794263","display_name":null,"funder_award_id":"572760/508","funder_id":"https://openalex.org/F4320323435","funder_display_name":"University of Kashan"}],"funders":[{"id":"https://openalex.org/F4320323435","display_name":"University of Kashan","ror":"https://ror.org/015zmr509"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W14896665","https://openalex.org/W105367266","https://openalex.org/W154962059","https://openalex.org/W1708699344","https://openalex.org/W1966976508","https://openalex.org/W1976891005","https://openalex.org/W2002369853","https://openalex.org/W2029553938","https://openalex.org/W2065534534","https://openalex.org/W2083129560","https://openalex.org/W2104917052","https://openalex.org/W2122187529","https://openalex.org/W2131529378","https://openalex.org/W2195864695","https://openalex.org/W2258992320","https://openalex.org/W2466967918","https://openalex.org/W2575894084","https://openalex.org/W2766874029"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W3111310291"],"abstract_inverted_index":{"The":[0,65],"irregularity":[1],"of":[2,21,35,42,68,90],"a":[3,22],"graph":[4],"[Formula:":[5,11,15,24,28,36,44,55,83,95,98,102],"see":[6,12,16,25,29,37,45,56,84,96,99,103],"text]":[7,17,26,30,100],"is":[8,31,71],"defined":[9],"as":[10],"text],":[13,97,104],"where":[14],"denotes":[18],"the":[19,32,40,51,63,74,77,88,91],"degree":[20],"vertex":[23],"and":[27,80,101],"edge":[33],"set":[34],"text].":[38],"From":[39],"class":[41,93],"all":[43,87],"text]-vertex":[46],"(molecular)":[47],"trees,":[48],"graphs":[49,75],"with":[50,76],"first":[52],"five":[53],"minimal":[54,82],"text]-values":[57,85],"have":[58],"already":[59],"been":[60],"characterized":[61],"in":[62],"literature.":[64],"main":[66],"purpose":[67],"this":[69],"paper":[70],"to":[72],"determine":[73],"sixth,":[78],"seventh":[79],"eighth":[81],"among":[86],"members":[89],"aforementioned":[92],"for":[94],"respectively.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}