{"id":"https://openalex.org/W4396917295","doi":"https://doi.org/10.1051/ro/2024111","title":"Spectral properties of Sombor matrix of threshold graphs","display_name":"Spectral properties of Sombor matrix of threshold graphs","publication_year":2024,"publication_date":"2024-05-15","ids":{"openalex":"https://openalex.org/W4396917295","doi":"https://doi.org/10.1051/ro/2024111"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2024111","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024111","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/forth/ro240025.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/forth/ro240025.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066661813","display_name":"Bilal Ahmad Rather","orcid":"https://orcid.org/0000-0003-1381-0291"},"institutions":[{"id":"https://openalex.org/I201726411","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862","country_code":"AE","type":"education","lineage":["https://openalex.org/I201726411"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Bilal Ahmad Rather","raw_affiliation_strings":["Department of Mathematical Sciences , College of Science , United Arab Emirate University , Al Ain 15551 , UAE"],"raw_orcid":"https://orcid.org/0000-0003-1381-0291","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , College of Science , United Arab Emirate University , Al Ain 15551 , UAE","institution_ids":["https://openalex.org/I201726411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024364073","display_name":"Muhammad Imran","orcid":"https://orcid.org/0000-0002-2827-0462"},"institutions":[{"id":"https://openalex.org/I201726411","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862","country_code":"AE","type":"education","lineage":["https://openalex.org/I201726411"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Muhammad Imran","raw_affiliation_strings":["Department of Mathematical Sciences , College of Science , United Arab Emirate University , Al Ain 15551 , UAE"],"raw_orcid":"https://orcid.org/0000-0002-2827-0462","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , College of Science , United Arab Emirate University , Al Ain 15551 , UAE","institution_ids":["https://openalex.org/I201726411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003523270","display_name":"Zahid Raza","orcid":"https://orcid.org/0000-0002-4910-2038"},"institutions":[{"id":"https://openalex.org/I29891158","display_name":"University of Sharjah","ror":"https://ror.org/00engpz63","country_code":"AE","type":"education","lineage":["https://openalex.org/I29891158"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Zahid Raza","raw_affiliation_strings":["Department of Mathematics , College of Sciences , University of Sharjah , Sharjah , UAE"],"raw_orcid":"https://orcid.org/0000-0002-4910-2038","affiliations":[{"raw_affiliation_string":"Department of Mathematics , College of Sciences , University of Sharjah , Sharjah , UAE","institution_ids":["https://openalex.org/I29891158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063558926","display_name":"Fozia Bashir Farooq","orcid":"https://orcid.org/0000-0002-2144-5098"},"institutions":[{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Fozia Bashir Farooq","raw_affiliation_strings":["Department of Mathematics and Statistics , College of Science , Imam Mohammad Ibn Saud Islamic University , Riyadh , Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , College of Science , Imam Mohammad Ibn Saud Islamic University , Riyadh , Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":null,"fwci":2.3993,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.86920158,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"58","issue":"4","first_page":"2845","last_page":"2864"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9864000082015991,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9667999744415283,"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/spectral-properties","display_name":"Spectral properties","score":0.5224384665489197},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4543165862560272},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42639926075935364},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3336505889892578},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2571920156478882},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.2406977415084839},{"id":"https://openalex.org/keywords/astrophysics","display_name":"Astrophysics","score":0.10259899497032166},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.08712932467460632}],"concepts":[{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.5224384665489197},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4543165862560272},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42639926075935364},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3336505889892578},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2571920156478882},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.2406977415084839},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.10259899497032166},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.08712932467460632}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2024111","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024111","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/forth/ro240025.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:edpsciences.org:dkey/10.1051/ro/2024111","is_oa":false,"landing_page_url":"https://www.rairo-ro.org/10.1051/ro/2024111/pdf","pdf_url":"https://www.rairo-ro.org/10.1051/ro/2024111/pdf","source":{"id":"https://openalex.org/S4306400744","display_name":"Springer Link (Chiba Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8488066","host_organization_name":"Chiba Institute of Technology","host_organization_lineage":["https://openalex.org/I8488066"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1051/ro/2024111","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1051/ro/2024111","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024111","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/forth/ro240025.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1962494971","display_name":null,"funder_award_id":"IMSIU-RP23073","funder_id":"https://openalex.org/F4320325415","funder_display_name":"Al-Imam Muhammad Ibn Saud Islamic University"}],"funders":[{"id":"https://openalex.org/F4320325415","display_name":"Al-Imam Muhammad Ibn Saud Islamic University","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4396917295.pdf","grobid_xml":"https://content.openalex.org/works/W4396917295.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1974430377","https://openalex.org/W2051481353","https://openalex.org/W2056947900","https://openalex.org/W2069186987","https://openalex.org/W2345923353","https://openalex.org/W2609437223","https://openalex.org/W2912916739","https://openalex.org/W2963984541","https://openalex.org/W2996717897","https://openalex.org/W3119697211","https://openalex.org/W3128182610","https://openalex.org/W3128911204","https://openalex.org/W3131911019","https://openalex.org/W3184725411","https://openalex.org/W3203952454","https://openalex.org/W4200320807","https://openalex.org/W4200375956","https://openalex.org/W4206391798","https://openalex.org/W4213217223","https://openalex.org/W4230572909","https://openalex.org/W4281756048","https://openalex.org/W4291129530","https://openalex.org/W4291899080","https://openalex.org/W4311220531","https://openalex.org/W4381085822","https://openalex.org/W4384129556","https://openalex.org/W4390542631"],"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/W2600246793","https://openalex.org/W2319316188"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,12,17,31,37,40,51,57,62,65,70,76,78],"Sombor":[3,13,18,25,33,41,58,66],"spectral":[4],"properties":[5],"of":[6,39,50,72],"threshold":[7],"graphs,":[8],"a":[9],"formula":[10],"for":[11,46,87],"index":[14],"is":[15],"presented,":[16,36],"eigenvalues":[19,26,34,42],"are":[20,27,35,43,55,85],"given,":[21,56],"graphs":[22],"with":[23,69],"simple":[24],"characterized,":[28],"bounds":[29,63],"on":[30,64],"smallest/largest":[32],"multiplicities":[38],"discussed,":[44],"formulae":[45],"trace":[47],"and":[48,61,90],"determinant":[49],"associated":[52],"quotient":[53],"matrix":[54,89],"spread":[59],"bound":[60],"energy":[67],"along":[68],"characterization":[71],"extremal":[73],"graphs.":[74],"At":[75],"end,":[77],"conclusion":[79],"states":[80],"that":[81],"all":[82],"our":[83],"results":[84],"valid":[86],"adjacency":[88,92],"other":[91],"type":[93],"matrices.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
