{"id":"https://openalex.org/W4308558686","doi":"https://doi.org/10.1155/2022/8202681","title":"On the Maximum Sombor Index of Unicyclic Graphs with a Fixed Girth","display_name":"On the Maximum Sombor Index of Unicyclic Graphs with a Fixed Girth","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4308558686","doi":"https://doi.org/10.1155/2022/8202681"},"language":"en","primary_location":{"id":"doi:10.1155/2022/8202681","doi":"https://doi.org/10.1155/2022/8202681","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/8202681","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/2022/8202681","source":{"id":"https://openalex.org/S2764668616","display_name":"Journal of Mathematics","issn_l":"2314-4629","issn":["2314-4629","2314-4785"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/2022/8202681","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104669071","display_name":"B. Senthilkumar","orcid":"https://orcid.org/0000-0001-8121-7233","observed_orcids":["https://orcid.org/0000-0001-8121-7233"]},"institutions":[{"id":"https://openalex.org/I932239252","display_name":"SASTRA University","ror":"https://ror.org/032jk8892","country_code":"IN","type":"education","lineage":["https://openalex.org/I932239252"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"B. Senthilkumar","raw_affiliation_strings":["Department of Mathematics, SASTRA Deemed University, Thanjavur, India sastra.edu","Department of Mathematics, SASTRA Deemed University, Thanjavur"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, SASTRA Deemed University, Thanjavur, India sastra.edu","institution_ids":["https://openalex.org/I932239252"]},{"raw_affiliation_string":"Department of Mathematics, SASTRA Deemed University, Thanjavur","institution_ids":["https://openalex.org/I932239252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043202535","display_name":"Yanamandram Balasubramanian Venkatakrishnan","orcid":"https://orcid.org/0000-0003-4560-2040","observed_orcids":["https://orcid.org/0000-0003-4560-2040"]},"institutions":[{"id":"https://openalex.org/I932239252","display_name":"SASTRA University","ror":"https://ror.org/032jk8892","country_code":"IN","type":"education","lineage":["https://openalex.org/I932239252"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Y. B. Venkatakrishnan","raw_affiliation_strings":["Department of Mathematics, SASTRA Deemed University, Thanjavur, India sastra.edu","Department of Mathematics, SASTRA Deemed University, Thanjavur"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, SASTRA Deemed University, Thanjavur, India sastra.edu","institution_ids":["https://openalex.org/I932239252"]},{"raw_affiliation_string":"Department of Mathematics, SASTRA Deemed University, Thanjavur","institution_ids":["https://openalex.org/I932239252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051054037","display_name":"Selvaraj Balachandran","orcid":"https://orcid.org/0000-0003-2782-6315","observed_orcids":["https://orcid.org/0000-0003-2782-6315","https://orcid.org/0000-0001-8498-3822"]},"institutions":[{"id":"https://openalex.org/I932239252","display_name":"SASTRA University","ror":"https://ror.org/032jk8892","country_code":"IN","type":"education","lineage":["https://openalex.org/I932239252"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"S. Balachandran","raw_affiliation_strings":["Department of Mathematics, SASTRA Deemed University, Thanjavur, India sastra.edu","Department of Mathematics, SASTRA Deemed University, Thanjavur"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, SASTRA Deemed University, Thanjavur, India sastra.edu","institution_ids":["https://openalex.org/I932239252"]},{"raw_affiliation_string":"Department of Mathematics, SASTRA Deemed University, Thanjavur","institution_ids":["https://openalex.org/I932239252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046231788","display_name":"Akbar Ali","orcid":"https://orcid.org/0000-0001-8160-4196","observed_orcids":["https://orcid.org/0000-0001-8160-4196"]},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Akbar Ali","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il, Saudi Arabia uoh.edu.sa","Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il"],"raw_orcid":"https://orcid.org/0000-0001-8160-4196","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il, Saudi Arabia uoh.edu.sa","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013716670","display_name":"Tariq Alraqad","orcid":"https://orcid.org/0000-0002-8881-4812","observed_orcids":["https://orcid.org/0000-0002-8881-4812"]},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Tariq A. Alraqad","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il, Saudi Arabia uoh.edu.sa","Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il"],"raw_orcid":"https://orcid.org/0000-0002-8881-4812","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il, Saudi Arabia uoh.edu.sa","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054703556","display_name":"Amjad E. Hamza","orcid":"https://orcid.org/0000-0002-8001-1548","observed_orcids":["https://orcid.org/0000-0002-8001-1548"]},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Amjad E. Hamza","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il, Saudi Arabia uoh.edu.sa","Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il, Saudi Arabia uoh.edu.sa","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il","institution_ids":["https://openalex.org/I4210088963"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046231788"],"corresponding_institution_ids":["https://openalex.org/I4210088963"],"apc_list":{"value":2160,"currency":"USD","value_usd":2160},"apc_paid":{"value":2160,"currency":"USD","value_usd":2160},"fwci":1.1112,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.70476335,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2022","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":1.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":9.999999747378752e-05,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.0,"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/sombor-index","display_name":"Sombor index","score":0.9850000143051147},{"id":"https://openalex.org/keywords/unicyclic-graphs","display_name":"unicyclic graphs","score":0.9879999756813049},{"id":"https://openalex.org/keywords/girth","display_name":"girth","score":0.9150000214576721},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"extremal graph theory","score":0.8529999852180481},{"id":"https://openalex.org/keywords/topological-indices","display_name":"topological indices","score":0.7120000123977661},{"id":"https://openalex.org/keywords/graph-characterization","display_name":"graph characterization","score":0.37299999594688416},{"id":"https://openalex.org/keywords/degree-sequences","display_name":"degree sequences","score":0.32199999690055847}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6065294146537781},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5288794040679932}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2022/8202681","doi":"https://doi.org/10.1155/2022/8202681","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/8202681","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/2022/8202681","source":{"id":"https://openalex.org/S2764668616","display_name":"Journal of Mathematics","issn_l":"2314-4629","issn":["2314-4629","2314-4785"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jjmath:8202681","doi":null,"is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/jmath/2022/8202681.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:5a0c6a39f5be4345b19f9a6c3eb42b23","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/5a0c6a39f5be4345b19f9a6c3eb42b23","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,"listed_in":[],"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":"Journal of Mathematics, Vol 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/8202681","doi":"https://doi.org/10.1155/2022/8202681","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/8202681","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/2022/8202681","source":{"id":"https://openalex.org/S2764668616","display_name":"Journal of Mathematics","issn_l":"2314-4629","issn":["2314-4629","2314-4785"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2477055178","display_name":null,"funder_award_id":"RG-22005","funder_id":"https://openalex.org/F4320325395","funder_display_name":"University of Hail"}],"funders":[{"id":"https://openalex.org/F4320325395","display_name":"University of Hail","ror":"https://ror.org/013w98a82"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4308558686.pdf","grobid_xml":"https://content.openalex.org/works/W4308558686.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W2899210285","https://openalex.org/W3128182610","https://openalex.org/W3131911019","https://openalex.org/W3134545247","https://openalex.org/W3136501028","https://openalex.org/W4213214460","https://openalex.org/W4220940703","https://openalex.org/W4223940661","https://openalex.org/W4232896595","https://openalex.org/W4281483735","https://openalex.org/W4292289436","https://openalex.org/W7005936725"],"related_works":["https://openalex.org/W4387418577","https://openalex.org/W4407973065","https://openalex.org/W3185051779","https://openalex.org/W4408944760","https://openalex.org/W4407601499","https://openalex.org/W4400962143","https://openalex.org/W4223940661","https://openalex.org/W4289550777","https://openalex.org/W4311726692","https://openalex.org/W4392887018"],"abstract_inverted_index":{"Let":[0],"G":[1,27,41],"be":[2],"a":[3,17,35,39,63,93],"graph":[4,40,51],"having":[5],"the":[6,14,45,53,70,73,76,81,85],"set":[7],"of":[8,16,20,26,34,47,72,80,87],"edges":[9],"E(G).":[10],"Represent":[11],"by":[12],"dG(u)":[13],"degree":[15],"vertex":[18],"u":[19],"G.":[21,48],"The":[22,32],"Sombor":[23],"(SO)":[24],"index":[25,83],"is":[28,42,58],"defined":[29],"as":[30,44,62],".":[31],"length":[33],"shortest":[36],"cycle":[37],"in":[38,84],"known":[43],"girth":[46,95],"A":[49],"connected":[50],"with":[52,92],"same":[54],"order":[55],"and":[56,96],"size":[57],"usually":[59],"referred":[60],"to":[61],"(connected)":[64,89],"unicyclic":[65,90],"graph.":[66],"This":[67],"paper":[68],"reports":[69],"characterization":[71],"graphs":[74,91],"possessing":[75],"first\u2010two":[77],"maximum":[78],"values":[79],"SO":[82],"class":[86],"all":[88],"fixed":[94],"order.":[97]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-11-12T00:00:00"}
