{"id":"https://openalex.org/W4405231916","doi":"https://doi.org/10.1142/s1793830925500077","title":"Some properties of proper power graphs in finite Abelian groups","display_name":"Some properties of proper power graphs in finite Abelian groups","publication_year":2024,"publication_date":"2024-12-10","ids":{"openalex":"https://openalex.org/W4405231916","doi":"https://doi.org/10.1142/s1793830925500077"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830925500077","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830925500077","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093775168","display_name":"G. Dhawlath","orcid":null},"institutions":[{"id":"https://openalex.org/I4210131147","display_name":"SRM University","ror":"https://ror.org/037skf023","country_code":"IN","type":"education","lineage":["https://openalex.org/I145286018","https://openalex.org/I4210131147"]},{"id":"https://openalex.org/I4401726783","display_name":"VIT-AP University","ror":"https://ror.org/007v4hf75","country_code":null,"type":"education","lineage":["https://openalex.org/I4401726783"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"G. Dhawlath","raw_affiliation_strings":["Department of Mathematics, School of Advanced Sciences, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati, AP, India"],"raw_orcid":"https://orcid.org/0009-0002-5488-7316","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Advanced Sciences, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati, AP, India","institution_ids":["https://openalex.org/I4210131147","https://openalex.org/I4401726783"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112215689","display_name":"V. Sudheer Raja","orcid":null},"institutions":[{"id":"https://openalex.org/I4210131147","display_name":"SRM University","ror":"https://ror.org/037skf023","country_code":"IN","type":"education","lineage":["https://openalex.org/I145286018","https://openalex.org/I4210131147"]},{"id":"https://openalex.org/I4401726783","display_name":"VIT-AP University","ror":"https://ror.org/007v4hf75","country_code":null,"type":"education","lineage":["https://openalex.org/I4401726783"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"V. Raja","raw_affiliation_strings":["Department of Mathematics, School of Advanced Sciences, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati, AP, India"],"raw_orcid":"https://orcid.org/0000-0003-1460-4270","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Advanced Sciences, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati, AP, India","institution_ids":["https://openalex.org/I4210131147","https://openalex.org/I4401726783"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5093775168"],"corresponding_institution_ids":["https://openalex.org/I4210131147","https://openalex.org/I4401726783"],"apc_list":null,"apc_paid":null,"fwci":0.3329,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.65869762,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"17","issue":"08","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9866999983787537,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9866999983787537,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9800999760627747,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.972000002861023,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.8753410577774048},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6773005723953247},{"id":"https://openalex.org/keywords/rank-of-an-abelian-group","display_name":"Rank of an abelian group","score":0.5485135912895203},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48515352606773376},{"id":"https://openalex.org/keywords/elementary-abelian-group","display_name":"Elementary abelian group","score":0.4651309847831726},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40228021144866943}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8753410577774048},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6773005723953247},{"id":"https://openalex.org/C200681373","wikidata":"https://www.wikidata.org/wiki/Q1260803","display_name":"Rank of an abelian group","level":4,"score":0.5485135912895203},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48515352606773376},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.4651309847831726},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40228021144866943}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830925500077","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830925500077","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1559988265","https://openalex.org/W1981580608","https://openalex.org/W2036534180","https://openalex.org/W2120565842","https://openalex.org/W2172271296","https://openalex.org/W2963403635","https://openalex.org/W4213144751"],"related_works":["https://openalex.org/W1999189963","https://openalex.org/W2708535589","https://openalex.org/W2009465652","https://openalex.org/W37379289","https://openalex.org/W2004460156","https://openalex.org/W2070941974","https://openalex.org/W3017700689","https://openalex.org/W3202796508","https://openalex.org/W4200381501","https://openalex.org/W2109426599"],"abstract_inverted_index":{"The":[0,52],"power":[1,55,102],"graph":[2,18,56],"of":[3,57,87,113,131],"a":[4,15,70,106],"group":[5],"[Formula:":[6,11,24,29,36,46,58,65,81,114],"see":[7,12,25,30,37,47,59,66,82,115],"text],":[8,13],"denoted":[9,79],"as":[10,80],"constitutes":[14],"simple":[16],"undirected":[17],"characterized":[19],"by":[20,45,63],"its":[21],"vertex":[22,71,132],"set":[23],"text].":[26,83],"Specifically,":[27],"vertices":[28],"text]":[31,38,48,60,67,116],"exhibit":[32],"adjacency":[33],"exclusively":[34],"if":[35],"belongs":[39],"to":[40,73],"the":[41,74,85,94,100,111,129],"cyclic":[42],"subgroup":[43],"generated":[44],"or":[49],"vice":[50],"versa.":[51],"corresponding":[53,72],"proper":[54,101],"is":[61,78,121],"obtained":[62],"taking":[64],"and":[68,96,135],"removing":[69],"identity":[75],"element,":[76],"which":[77],"In":[84],"context":[86],"finite":[88,118],"abelian":[89,119],"groups,":[90],"this":[91],"paper":[92,126],"establishes":[93],"sufficient":[95],"necessary":[97],"conditions":[98],"for":[99,110],"graph\u2019s":[103],"connectedness.":[104],"Moreover,":[105],"precise":[107],"upper":[108],"bound":[109],"diameter":[112],"in":[117],"groups":[120],"provided":[122],"with":[123],"sharpness.":[124],"This":[125],"also":[127],"explores":[128],"study":[130],"connectivity,":[133],"center,":[134],"planarity.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}