{"id":"https://openalex.org/W3088159001","doi":"https://doi.org/10.3390/sym12101591","title":"Extremal Trees with Respect to the Difference between Atom-Bond Connectivity Index and Randi\u0107 Index","display_name":"Extremal Trees with Respect to the Difference between Atom-Bond Connectivity Index and Randi\u0107 Index","publication_year":2020,"publication_date":"2020-09-25","ids":{"openalex":"https://openalex.org/W3088159001","doi":"https://doi.org/10.3390/sym12101591","mag":"3088159001"},"language":"en","primary_location":{"id":"doi:10.3390/sym12101591","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12101591","pdf_url":"https://www.mdpi.com/2073-8994/12/10/1591/pdf?version=1601010553","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/2073-8994/12/10/1591/pdf?version=1601010553","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058803093","display_name":"Wan Nor Nabila Nadia Wan Zuki","orcid":null},"institutions":[{"id":"https://openalex.org/I157696592","display_name":"Universiti Malaysia Terengganu","ror":"https://ror.org/02474f074","country_code":"MY","type":"education","lineage":["https://openalex.org/I157696592"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Wan Nor Nabila Nadia Wan Zuki","raw_affiliation_strings":["Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia","institution_ids":["https://openalex.org/I157696592"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004929939","display_name":"Zhibin Du","orcid":"https://orcid.org/0000-0001-5795-3580"},"institutions":[{"id":"https://openalex.org/I183816158","display_name":"Zhaoqing University","ror":"https://ror.org/025n5kj18","country_code":"CN","type":"education","lineage":["https://openalex.org/I183816158"]},{"id":"https://openalex.org/I187400657","display_name":"South China Normal University","ror":"https://ror.org/01kq0pv72","country_code":"CN","type":"education","lineage":["https://openalex.org/I187400657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhibin Du","raw_affiliation_strings":["School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China","School of Software, South China Normal University, Foshan 528225, China"],"raw_orcid":"https://orcid.org/0000-0001-5795-3580","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China","institution_ids":["https://openalex.org/I183816158"]},{"raw_affiliation_string":"School of Software, South China Normal University, Foshan 528225, China","institution_ids":["https://openalex.org/I187400657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066651205","display_name":"Muhammad Kamran Jamil","orcid":"https://orcid.org/0000-0001-5715-9299"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Kamran Jamil","raw_affiliation_strings":["Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore 46000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore 46000, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079555077","display_name":"Roslan Hasni","orcid":"https://orcid.org/0000-0003-3695-2145"},"institutions":[{"id":"https://openalex.org/I157696592","display_name":"Universiti Malaysia Terengganu","ror":"https://ror.org/02474f074","country_code":"MY","type":"education","lineage":["https://openalex.org/I157696592"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Roslan Hasni","raw_affiliation_strings":["Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia","institution_ids":["https://openalex.org/I157696592"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5079555077"],"corresponding_institution_ids":["https://openalex.org/I157696592"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.387,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.59831944,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"12","issue":"10","first_page":"1591","last_page":"1591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9983000159263611,"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/T12023","display_name":"Cholinesterase and Neurodegenerative Diseases","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2736","display_name":"Pharmacology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/topological-index","display_name":"Topological index","score":0.9322780966758728},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7102753520011902},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.6039137840270996},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5520487427711487},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.50943523645401},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.48501846194267273},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.484384149312973},{"id":"https://openalex.org/keywords/mathematical-chemistry","display_name":"Mathematical chemistry","score":0.45850780606269836},{"id":"https://openalex.org/keywords/atom","display_name":"Atom (system on chip)","score":0.4510681629180908},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20611006021499634}],"concepts":[{"id":"https://openalex.org/C159867001","wikidata":"https://www.wikidata.org/wiki/Q904942","display_name":"Topological index","level":2,"score":0.9322780966758728},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7102753520011902},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.6039137840270996},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5520487427711487},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.50943523645401},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.48501846194267273},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.484384149312973},{"id":"https://openalex.org/C158808287","wikidata":"https://www.wikidata.org/wiki/Q2556886","display_name":"Mathematical chemistry","level":2,"score":0.45850780606269836},{"id":"https://openalex.org/C58312451","wikidata":"https://www.wikidata.org/wiki/Q4817200","display_name":"Atom (system on chip)","level":2,"score":0.4510681629180908},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20611006021499634},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12101591","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12101591","pdf_url":"https://www.mdpi.com/2073-8994/12/10/1591/pdf?version=1601010553","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:9d00f79d85b540f688ab3fafb1a9875c","is_oa":true,"landing_page_url":"https://doaj.org/article/9d00f79d85b540f688ab3fafb1a9875c","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 10, p 1591 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/10/1591/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12101591","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/sym12101591","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12101591","pdf_url":"https://www.mdpi.com/2073-8994/12/10/1591/pdf?version=1601010553","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":[{"id":"https://openalex.org/G243728567","display_name":null,"funder_award_id":"55192/6","funder_id":"https://openalex.org/F4320327340","funder_display_name":"Universiti Malaysia Terengganu"}],"funders":[{"id":"https://openalex.org/F4320327340","display_name":"Universiti Malaysia Terengganu","ror":"https://ror.org/02474f074"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3088159001.pdf","grobid_xml":"https://content.openalex.org/works/W3088159001.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W623814603","https://openalex.org/W822886830","https://openalex.org/W1545231783","https://openalex.org/W1755385997","https://openalex.org/W1973453175","https://openalex.org/W1992044995","https://openalex.org/W2011558844","https://openalex.org/W2021229217","https://openalex.org/W2041735011","https://openalex.org/W2076121179","https://openalex.org/W2088743362","https://openalex.org/W2090484032","https://openalex.org/W2189321692","https://openalex.org/W2341939561","https://openalex.org/W2570858210","https://openalex.org/W2576293399","https://openalex.org/W2742977978","https://openalex.org/W2743718144","https://openalex.org/W2931354686","https://openalex.org/W2940853631","https://openalex.org/W2962752362","https://openalex.org/W3099343054","https://openalex.org/W6687151571","https://openalex.org/W6703784367","https://openalex.org/W6732013410","https://openalex.org/W6742726193"],"related_works":["https://openalex.org/W4401082530","https://openalex.org/W2000076674","https://openalex.org/W2066891982","https://openalex.org/W2909285183","https://openalex.org/W2765701138","https://openalex.org/W2996166442","https://openalex.org/W2337701229","https://openalex.org/W3088159001","https://openalex.org/W3198901130","https://openalex.org/W2262329689"],"abstract_inverted_index":{"Let":[0],"G":[1],"be":[2],"a":[3],"simple,":[4],"connected":[5],"and":[6,14,28,37,53,65],"undirected":[7],"graph.":[8],"The":[9,89],"atom-bond":[10,35],"connectivity":[11,36],"index":[12,16,79],"(ABC(G))":[13],"Randi\u0107":[15,38],"(R(G))":[17],"are":[18],"the":[19,32,49,51,54,67],"two":[20],"most":[21],"well":[22],"known":[23],"topological":[24],"indices.":[25],"Recently,":[26],"Ali":[27],"Du":[29],"(2017)":[30],"introduced":[31],"difference":[33],"between":[34],"indices,":[39],"denoted":[40],"as":[41],"ABC\u2212R":[42,61,78],"index.":[43],"In":[44],"this":[45],"paper,":[46],"we":[47],"determine":[48],"fourth,":[50],"fifth":[52],"sixth":[55],"maximum":[56],"chemical":[57,63,104],"trees":[58,82],"values":[59],"of":[60,80,86,91,99],"for":[62,77],"trees,":[64],"characterize":[66],"corresponding":[68],"extremal":[69],"graphs.":[70],"We":[71],"also":[72],"obtain":[73],"an":[74],"upper":[75],"bound":[76],"such":[81],"with":[83],"given":[84],"number":[85],"pendant":[87],"vertices.":[88],"role":[90],"symmetry":[92],"has":[93],"great":[94],"importance":[95],"in":[96,103],"different":[97],"areas":[98],"graph":[100,105],"theory":[101],"especially":[102],"theory.":[106]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
