{"id":"https://openalex.org/W4389780573","doi":"https://doi.org/10.3390/axioms12121128","title":"Spectral Analysis of the Adjacency Matrices for Alternating Quotients of Hyperbolic Triangle Group \u25b5*(3,q,r) for q < r Primes","display_name":"Spectral Analysis of the Adjacency Matrices for Alternating Quotients of Hyperbolic Triangle Group \u25b5*(3,q,r) for q < r Primes","publication_year":2023,"publication_date":"2023-12-15","ids":{"openalex":"https://openalex.org/W4389780573","doi":"https://doi.org/10.3390/axioms12121128"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12121128","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms12121128","pdf_url":"https://www.mdpi.com/2075-1680/12/12/1128/pdf?version=1702653746","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/2075-1680/12/12/1128/pdf?version=1702653746","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093504545","display_name":"Sajida Younas","orcid":null},"institutions":[{"id":"https://openalex.org/I121243025","display_name":"International Islamic University, Islamabad","ror":"https://ror.org/047w75g40","country_code":"PK","type":"education","lineage":["https://openalex.org/I121243025"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Sajida Younas","raw_affiliation_strings":["Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan","Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I121243025"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan;","institution_ids":["https://openalex.org/I121243025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034475737","display_name":"Sajida Kousar","orcid":"https://orcid.org/0000-0001-8157-7909"},"institutions":[{"id":"https://openalex.org/I121243025","display_name":"International Islamic University, Islamabad","ror":"https://ror.org/047w75g40","country_code":"PK","type":"education","lineage":["https://openalex.org/I121243025"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Sajida Kousar","raw_affiliation_strings":["Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan","Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan;"],"raw_orcid":"https://orcid.org/0000-0001-8157-7909","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I121243025"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan;","institution_ids":["https://openalex.org/I121243025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090639857","display_name":"Majed Albaity","orcid":"https://orcid.org/0000-0001-6599-5975"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Majed Albaity","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80348, Jeddah 22254, Saudi Arabia","Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80348, Jeddah 22254, Saudi Arabia;"],"raw_orcid":"https://orcid.org/0000-0001-6599-5975","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80348, Jeddah 22254, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80348, Jeddah 22254, Saudi Arabia;","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100646948","display_name":"Tahir Mahmood","orcid":"https://orcid.org/0000-0002-3871-3845"},"institutions":[{"id":"https://openalex.org/I121243025","display_name":"International Islamic University, Islamabad","ror":"https://ror.org/047w75g40","country_code":"PK","type":"education","lineage":["https://openalex.org/I121243025"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Tahir Mahmood","raw_affiliation_strings":["Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan","Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan;"],"raw_orcid":"https://orcid.org/0000-0002-3871-3845","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I121243025"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan;","institution_ids":["https://openalex.org/I121243025"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100646948"],"corresponding_institution_ids":["https://openalex.org/I121243025"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30566667,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"12","first_page":"1128","last_page":"1128"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9994000196456909,"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/T10849","display_name":"Finite Group Theory Research","score":0.9994000196456909,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9929999709129333,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7845370769500732},{"id":"https://openalex.org/keywords/coset","display_name":"Coset","score":0.7248685359954834},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5822785496711731},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.512691855430603},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.4779941141605377},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.47540029883384705},{"id":"https://openalex.org/keywords/relatively-hyperbolic-group","display_name":"Relatively hyperbolic group","score":0.46014273166656494},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4507168233394623},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.4422356188297272},{"id":"https://openalex.org/keywords/hyperbolic-geometry","display_name":"Hyperbolic geometry","score":0.4197801351547241},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21725627779960632},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.2003568410873413},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17380291223526},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.1578344702720642},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.10887771844863892},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0906655490398407}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7845370769500732},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.7248685359954834},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5822785496711731},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.512691855430603},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.4779941141605377},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.47540029883384705},{"id":"https://openalex.org/C40020168","wikidata":"https://www.wikidata.org/wiki/Q7310818","display_name":"Relatively hyperbolic group","level":4,"score":0.46014273166656494},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4507168233394623},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.4422356188297272},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.4197801351547241},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21725627779960632},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.2003568410873413},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17380291223526},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.1578344702720642},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.10887771844863892},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0906655490398407},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12121128","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms12121128","pdf_url":"https://www.mdpi.com/2075-1680/12/12/1128/pdf?version=1702653746","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:15500487759b4ff0a8f83ea40461b95a","is_oa":true,"landing_page_url":"https://doaj.org/article/15500487759b4ff0a8f83ea40461b95a","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":"Axioms, Vol 12, Iss 12, p 1128 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/12/1128/","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12121128","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":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12121128","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms12121128","pdf_url":"https://www.mdpi.com/2075-1680/12/12/1128/pdf?version=1702653746","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4389780573.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1985911376","https://openalex.org/W1996788433","https://openalex.org/W2002653466","https://openalex.org/W2013737355","https://openalex.org/W2019085230","https://openalex.org/W2039009290","https://openalex.org/W2051873748","https://openalex.org/W2071091810","https://openalex.org/W2082203521","https://openalex.org/W2082834383","https://openalex.org/W2142879590","https://openalex.org/W2311457249","https://openalex.org/W2315615024","https://openalex.org/W2594379622","https://openalex.org/W2899006357","https://openalex.org/W2905544342","https://openalex.org/W2913837007","https://openalex.org/W2963428250","https://openalex.org/W2971696961","https://openalex.org/W2980478997","https://openalex.org/W2994530991","https://openalex.org/W3021754266","https://openalex.org/W3024240012","https://openalex.org/W3034287238","https://openalex.org/W3036433193","https://openalex.org/W3126682283","https://openalex.org/W4238580623","https://openalex.org/W4252813291"],"related_works":["https://openalex.org/W4213150077","https://openalex.org/W2369410163","https://openalex.org/W2059018062","https://openalex.org/W2604585036","https://openalex.org/W2078477160","https://openalex.org/W1989103179","https://openalex.org/W1991172810","https://openalex.org/W125803343","https://openalex.org/W2117632582","https://openalex.org/W2153421018"],"abstract_inverted_index":{"Hyperbolic":[0],"triangle":[1,26,69],"groups":[2,15],"are":[3,13],"found":[4],"within":[5],"the":[6,18,21,32,40,55,67,75],"category":[7],"of":[8,23,42,50,90,104],"finitely":[9,43],"generated":[10,44],"groups.":[11,45],"These":[12],"topological":[14],"formed":[16],"by":[17,100],"reflections":[19],"along":[20],"sides":[22],"a":[24,37,51,64,101],"hyperbolic":[25,33,68],"and":[27,74],"acting":[28],"properly":[29],"discontinuously":[30],"on":[31],"plane.":[34],"Higman":[35],"raised":[36],"question":[38],"about":[39],"simplicity":[41],"The":[46,78,88],"best":[47],"known":[48],"example":[49],"simple":[52],"group":[53,57,70],"is":[54,97],"alternating":[56,76],"An,":[58],"where":[59],"n\u22655.":[60],"This":[61],"article":[62],"establishes":[63],"relation":[65],"between":[66],"denoted":[71],"as":[72],"\u25b5*(3,7,r)":[73],"group.":[77],"approach":[79],"involves":[80],"employing":[81],"coset":[82,95],"diagrams":[83,96],"to":[84],"establish":[85],"this":[86],"connection.":[87],"construction":[89],"adjacency":[91],"matrices":[92],"for":[93],"these":[94],"performed,":[98],"followed":[99],"detailed":[102],"examination":[103],"their":[105],"spectral":[106],"characteristics.":[107]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2023-12-16T00:00:00"}