{"id":"https://openalex.org/W4408871939","doi":"https://doi.org/10.3390/axioms14040249","title":"Extremal Unicyclic Graphs for the Euler Sombor Index: Applications to Benzenoid Hydrocarbons and Drug Molecules","display_name":"Extremal Unicyclic Graphs for the Euler Sombor Index: Applications to Benzenoid Hydrocarbons and Drug Molecules","publication_year":2025,"publication_date":"2025-03-26","ids":{"openalex":"https://openalex.org/W4408871939","doi":"https://doi.org/10.3390/axioms14040249"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14040249","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040249","pdf_url":"https://www.mdpi.com/2075-1680/14/4/249/pdf?version=1742975895","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/4/249/pdf?version=1742975895","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090755071","display_name":"Zhenhua Su","orcid":"https://orcid.org/0000-0002-6957-610X"},"institutions":[{"id":"https://openalex.org/I12393601","display_name":"Huaihua University","ror":"https://ror.org/04zn6xq74","country_code":"CN","type":"education","lineage":["https://openalex.org/I12393601"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenhua Su","raw_affiliation_strings":["School of Mathematics and Computational Sciences, Huaihua University, Huaihua 418000, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Sciences, Huaihua University, Huaihua 418000, China","institution_ids":["https://openalex.org/I12393601"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019278713","display_name":"Zikai Tang","orcid":"https://orcid.org/0000-0002-2577-7890"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]},{"id":"https://openalex.org/I3130607311","display_name":"Changsha Normal University","ror":"https://ror.org/02sqk3z62","country_code":"CN","type":"education","lineage":["https://openalex.org/I3130607311"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zikai Tang","raw_affiliation_strings":["College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China","institution_ids":["https://openalex.org/I3130607311","https://openalex.org/I173759888"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019278713"],"corresponding_institution_ids":["https://openalex.org/I173759888","https://openalex.org/I3130607311"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":12.2842,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.98354302,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"14","issue":"4","first_page":"249","last_page":"249"},"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":0.992900013923645,"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/T13013","display_name":"Free Radicals and Antioxidants","score":0.9860000014305115,"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":0.5886240601539612},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49991917610168457},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.47060427069664},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.4470422863960266},{"id":"https://openalex.org/keywords/molecule","display_name":"Molecule","score":0.4281266927719116},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40880724787712097},{"id":"https://openalex.org/keywords/computational-chemistry","display_name":"Computational chemistry","score":0.3336635231971741},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3241286277770996},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.30212441086769104},{"id":"https://openalex.org/keywords/organic-chemistry","display_name":"Organic chemistry","score":0.1763714849948883},{"id":"https://openalex.org/keywords/world-wide-web","display_name":"World Wide Web","score":0.0918397307395935},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0864749550819397}],"concepts":[{"id":"https://openalex.org/C159867001","wikidata":"https://www.wikidata.org/wiki/Q904942","display_name":"Topological index","level":2,"score":0.5886240601539612},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49991917610168457},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.47060427069664},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.4470422863960266},{"id":"https://openalex.org/C32909587","wikidata":"https://www.wikidata.org/wiki/Q11369","display_name":"Molecule","level":2,"score":0.4281266927719116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40880724787712097},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.3336635231971741},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3241286277770996},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.30212441086769104},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.1763714849948883},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0918397307395935},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0864749550819397}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14040249","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040249","pdf_url":"https://www.mdpi.com/2075-1680/14/4/249/pdf?version=1742975895","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6dcca5c161954bf1b239aac127db20cc","is_oa":true,"landing_page_url":"https://doaj.org/article/6dcca5c161954bf1b239aac127db20cc","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 4, p 249 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14040249","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040249","pdf_url":"https://www.mdpi.com/2075-1680/14/4/249/pdf?version=1742975895","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1153809693","display_name":null,"funder_award_id":"2025JJ70485","funder_id":"https://openalex.org/F4320322866","funder_display_name":"Natural Science Foundation of Hainan Province"}],"funders":[{"id":"https://openalex.org/F4320322866","display_name":"Natural Science Foundation of Hainan Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4408871939.pdf"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W623814603","https://openalex.org/W3119697211","https://openalex.org/W3128182610","https://openalex.org/W3131911019","https://openalex.org/W3134545247","https://openalex.org/W4213442697","https://openalex.org/W4220940703","https://openalex.org/W4248104815","https://openalex.org/W4315433317","https://openalex.org/W4317373356","https://openalex.org/W4366608302","https://openalex.org/W4381853639","https://openalex.org/W4385381932","https://openalex.org/W4387418577","https://openalex.org/W4387796855","https://openalex.org/W4388196036","https://openalex.org/W4391503344","https://openalex.org/W4392566063","https://openalex.org/W4392887018","https://openalex.org/W4396633796","https://openalex.org/W4403366021","https://openalex.org/W4403734947","https://openalex.org/W4406864009","https://openalex.org/W6851948600","https://openalex.org/W6857142626","https://openalex.org/W6862967868","https://openalex.org/W6873756433"],"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/W2695410198","https://openalex.org/W4252064769","https://openalex.org/W2083597126"],"abstract_inverted_index":{"With":[0],"geometric":[1],"significance,":[2],"the":[3,18,37,42,55,64,80,91,99],"Euler":[4,43,92],"Sombor":[5,44,93],"index":[6,45,69,94],"of":[7,41,67,102],"a":[8],"graph":[9],"\u0393":[10],"is":[11],"defined":[12],"as":[13,52,54],"EP(\u0393)=\u2211{uv}\u2208E(\u0393)d(u)2+d(v)2+d(u)d(v).":[14],"It":[15],"originates":[16],"from":[17],"mathematical":[19],"distance":[20],"property":[21],"and":[22,39,74],"has":[23,95],"been":[24],"proven":[25],"to":[26],"have":[27],"good":[28],"chemical":[29],"applications":[30],"in":[31,98],"octane":[32],"isomers.":[33],"In":[34],"this":[35,68],"paper,":[36],"minimum":[38],"maximum":[40],"for":[46,70],"unicyclic":[47],"graphs":[48],"with":[49,79],"given":[50],"girth,":[51],"well":[53],"corresponding":[56],"extremal":[57],"graphs,":[58],"are":[59],"determined.":[60],"As":[61],"an":[62],"application,":[63],"experimental":[65],"values":[66],"some":[71],"benzenoid":[72],"hydrocarbons":[73],"drug":[75],"molecules":[76],"were":[77],"compared":[78],"boiling":[81],"point.":[82],"Through":[83],"regression":[84],"analysis,":[85],"it":[86],"was":[87],"further":[88],"demonstrated":[89],"that":[90],"excellent":[96],"predictability":[97],"physicochemical":[100],"properties":[101],"compounds.":[103]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
