{"id":"https://openalex.org/W4406767964","doi":"https://doi.org/10.3390/sym17020167","title":"Harmonic\u2013Arithmetic Index: Trees with Maximum Degrees and Comparative Analysis of Antidrugs","display_name":"Harmonic\u2013Arithmetic Index: Trees with Maximum Degrees and Comparative Analysis of Antidrugs","publication_year":2025,"publication_date":"2025-01-23","ids":{"openalex":"https://openalex.org/W4406767964","doi":"https://doi.org/10.3390/sym17020167"},"language":"en","primary_location":{"id":"doi:10.3390/sym17020167","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020167","pdf_url":"https://www.mdpi.com/2073-8994/17/2/167/pdf?version=1737623788","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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/2/167/pdf?version=1737623788","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101865894","display_name":"K.T. Ramesh","orcid":null},"institutions":[{"id":"https://openalex.org/I145286018","display_name":"SRM Institute of Science and Technology","ror":"https://ror.org/050113w36","country_code":"IN","type":"education","lineage":["https://openalex.org/I145286018"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kalpana Ramesh","raw_affiliation_strings":["Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India","institution_ids":["https://openalex.org/I145286018"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006461581","display_name":"S. Loganathan","orcid":null},"institutions":[{"id":"https://openalex.org/I145286018","display_name":"SRM Institute of Science and Technology","ror":"https://ror.org/050113w36","country_code":"IN","type":"education","lineage":["https://openalex.org/I145286018"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Shobana Loganathan","raw_affiliation_strings":["Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India","institution_ids":["https://openalex.org/I145286018"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006461581"],"corresponding_institution_ids":["https://openalex.org/I145286018"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":4.4911,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.87896564,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"17","issue":"2","first_page":"167","last_page":"167"},"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":0.9944000244140625,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9896000027656555,"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/mathematics","display_name":"Mathematics","score":0.6181368231773376},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5815296173095703},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.5647936463356018},{"id":"https://openalex.org/keywords/harmonic-mean","display_name":"Harmonic mean","score":0.44261014461517334},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.43237417936325073},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37728947401046753},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.32100316882133484},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3171288073062897},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1024315357208252}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6181368231773376},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5815296173095703},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.5647936463356018},{"id":"https://openalex.org/C203858083","wikidata":"https://www.wikidata.org/wiki/Q188347","display_name":"Harmonic mean","level":2,"score":0.44261014461517334},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.43237417936325073},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37728947401046753},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.32100316882133484},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3171288073062897},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1024315357208252},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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":2,"locations":[{"id":"doi:10.3390/sym17020167","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020167","pdf_url":"https://www.mdpi.com/2073-8994/17/2/167/pdf?version=1737623788","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:mdpi.com:/2073-8994/17/2/167/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym17020167","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":"Pages: 167","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym17020167","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020167","pdf_url":"https://www.mdpi.com/2073-8994/17/2/167/pdf?version=1737623788","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/W4406767964.pdf","grobid_xml":"https://content.openalex.org/works/W4406767964.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W2021229217","https://openalex.org/W2080255676","https://openalex.org/W2155875767","https://openalex.org/W2318794083","https://openalex.org/W4367049415","https://openalex.org/W4389752328","https://openalex.org/W4394725829","https://openalex.org/W4399613444"],"related_works":["https://openalex.org/W4376565614","https://openalex.org/W4384345245","https://openalex.org/W2790653811","https://openalex.org/W2128177177","https://openalex.org/W4244263057","https://openalex.org/W2096851309","https://openalex.org/W3092423828","https://openalex.org/W2984037143","https://openalex.org/W3015584308","https://openalex.org/W1491507776"],"abstract_inverted_index":{"Chemical":[0],"graph":[1,11,53,175,210],"theory":[2,176,211],"connects":[3,173],"the":[4,15,23,30,76,80,97,113,155,169,197],"analysis":[5],"of":[6,17,25,66,86,96],"molecular":[7,51,116,178,192],"structures":[8,117],"with":[9,89,177],"mathematical":[10,174],"theory,":[12],"allowing":[13],"for":[14,82,162,185],"prediction":[16],"chemical":[18,209],"and":[19,52,62,69,118,132,146,149,158,188,204,212],"physical":[20],"properties":[21],"through":[22],"use":[24],"topological":[26,105,130],"indices.":[27],"Among":[28],"these,":[29],"recently":[31],"introduced":[32],"Harmonic\u2013Arithmetic":[33],"(HA)":[34],"index,":[35],"proposed":[36],"by":[37,127],"Abeer":[38],"M.":[39],"Albalahi":[40],"et":[41],"al.":[42],"in":[43,71,111,123,207,218],"2023,":[44],"offers":[45],"a":[46,83,90,108,202],"novel":[47],"method":[48],"to":[49,101,153,215],"quantify":[50],"structures.":[54],"It":[55],"is":[56],"defined":[57],"as":[58,122,201],"HA(G)=\u2211\u03bc\u03c9\u2208E(G)4dG(\u03bc)dG(\u03c9)(dG(\u03bc)+dG(\u03c9))2,":[59],"where":[60,104],"dG(\u03bc)":[61],"dG(\u03c9)":[63],"are":[64],"degrees":[65],"nodes":[67],"\u03bc":[68],"\u03c9":[70],"G.":[72],"In":[73],"this":[74],"paper,":[75],"HA":[77,98,170,198],"index":[78,99,171],"examines":[79],"bounds":[81,184],"tree":[84,186],"T":[85],"order":[87],"n,":[88],"maximum":[91],"degree":[92],"\u2206.":[93],"The":[94,165],"application":[95],"extends":[100],"QSPR/QSAR":[102],"analyses,":[103],"indices":[106,131],"play":[107],"crucial":[109],"role":[110],"predicting":[112],"relationship":[114],"between":[115,142],"physicochemical":[119,163],"properties,":[120],"such":[121],"Parkinson\u2019s,":[124],"disease-related":[125],"antibiotics":[126],"calculating":[128],"their":[129],"analyzing":[133],"them":[134],"using":[135],"QSPR":[136],"models.":[137],"Comparative":[138],"analyses":[139],"were":[140],"performed":[141],"linear":[143],"regression":[144,151],"models":[145,152],"curvilinear-approach":[147],"quadratic":[148],"cubic":[150],"identify":[154],"minimal":[156],"RMSE":[157],"enhance":[159],"predictive":[160],"accuracy":[161],"properties.":[164,193],"results":[166],"demonstrate":[167],"that":[168],"effectively":[172],"characterization,":[179],"offering":[180],"reliable":[181],"predictions,":[182],"dependable":[183],"graphs,":[187],"meaningful":[189],"insights":[190],"into":[191],"These":[194],"findings":[195],"highlight":[196],"index\u2019s":[199],"potential":[200],"versatile":[203],"innovative":[205],"tool":[206],"advancing":[208],"its":[213],"applications":[214],"real-world":[216],"problems":[217],"chemistry.":[219]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
