{"id":"https://openalex.org/W2179833038","doi":"https://doi.org/10.1142/s1793830915500573","title":"The power digraphs associated with generalized dihedral groups","display_name":"The power digraphs associated with generalized dihedral groups","publication_year":2015,"publication_date":"2015-10-13","ids":{"openalex":"https://openalex.org/W2179833038","doi":"https://doi.org/10.1142/s1793830915500573","mag":"2179833038"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830915500573","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830915500573","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/A5025550983","display_name":"Uzma Ahmad","orcid":"https://orcid.org/0000-0001-5885-4437"},"institutions":[{"id":"https://openalex.org/I172780181","display_name":"University of the Punjab","ror":"https://ror.org/011maz450","country_code":"PK","type":"education","lineage":["https://openalex.org/I172780181"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Uzma Ahmad","raw_affiliation_strings":["University of the Punjab, Lahore, Pakistan"],"affiliations":[{"raw_affiliation_string":"University of the Punjab, Lahore, Pakistan","institution_ids":["https://openalex.org/I172780181"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025550983"],"corresponding_institution_ids":["https://openalex.org/I172780181"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.1136447,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"07","issue":"04","first_page":"1550057","last_page":"1550057"},"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/T10849","display_name":"Finite Group Theory Research","score":0.9983999729156494,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9961000084877014,"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/digraph","display_name":"Digraph","score":0.9389024972915649},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7591731548309326},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7537360191345215},{"id":"https://openalex.org/keywords/dihedral-group","display_name":"Dihedral group","score":0.7290648221969604},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7223532199859619},{"id":"https://openalex.org/keywords/dihedral-angle","display_name":"Dihedral angle","score":0.603100061416626},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4164174497127533},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4126087427139282},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.3141372799873352},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12838441133499146},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.12753582000732422},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09688767790794373}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.9389024972915649},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7591731548309326},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7537360191345215},{"id":"https://openalex.org/C72409365","wikidata":"https://www.wikidata.org/wiki/Q558339","display_name":"Dihedral group","level":3,"score":0.7290648221969604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7223532199859619},{"id":"https://openalex.org/C89025888","wikidata":"https://www.wikidata.org/wiki/Q911907","display_name":"Dihedral angle","level":4,"score":0.603100061416626},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4164174497127533},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4126087427139282},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3141372799873352},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12838441133499146},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.12753582000732422},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09688767790794373},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C112887158","wikidata":"https://www.wikidata.org/wiki/Q169324","display_name":"Hydrogen bond","level":3,"score":0.0},{"id":"https://openalex.org/C32909587","wikidata":"https://www.wikidata.org/wiki/Q11369","display_name":"Molecule","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830915500573","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830915500573","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W2016060847","https://openalex.org/W2056833032","https://openalex.org/W2076324096","https://openalex.org/W2091039147","https://openalex.org/W2599826197","https://openalex.org/W4236393932","https://openalex.org/W4402822554","https://openalex.org/W4402832228"],"related_works":["https://openalex.org/W2185332277","https://openalex.org/W2082494488","https://openalex.org/W2998116189","https://openalex.org/W2054349495","https://openalex.org/W2081358954","https://openalex.org/W2360655504","https://openalex.org/W2554461497","https://openalex.org/W2900665011","https://openalex.org/W4289752046","https://openalex.org/W2967056414"],"abstract_inverted_index":{"We":[0,93],"study":[1],"the":[2,13,17,29,40,64,70,75,78,80,88,130,136],"digraphs":[3,23,42,56,146],"based":[4],"on":[5],"dihedral":[6],"group":[7],"[Formula:":[8,25,34,46,121,125,147],"see":[9,26,35,47,122,126,148],"text]":[10,27,123,127,149],"by":[11,45],"using":[12],"power":[14,41,137,145],"mapping,":[15],"i.e.,":[16],"set":[18,30],"of":[19,21,31,54,66,72,77,82,84,90,110,120,132],"vertices":[20,113],"these":[22,55],"is":[24,33],"and":[28,43,51,87,97,124,135,143],"edges":[32],"text].":[36,48],"These":[37],"are":[38,57,150],"called":[39],"denoted":[44],"The":[49,108],"cycle":[50,73,106],"in-degree":[52],"structure":[53],"completely":[58,151],"examined.":[59],"This":[60],"investigation":[61],"leads":[62],"to":[63,103,128],"derivation":[65],"various":[67],"formulae":[68],"regarding":[69],"number":[71,81],"vertices,":[74,133],"length":[76],"cycles,":[79],"cycles":[83],"certain":[85],"lengths":[86],"in-degrees":[89],"all":[91,141],"vertices.":[92],"also":[94],"establish":[95],"necessary":[96],"sufficient":[98],"conditions":[99],"for":[100],"a":[101,105],"vertex":[102],"be":[104],"vertex.":[107],"analysis":[109],"distance":[111],"between":[112],"culminates":[114],"at":[115],"different":[116],"expressions":[117],"in":[118],"terms":[119],"determine":[129],"heights":[131],"components":[134],"digraph":[138],"itself.":[139],"Moreover,":[140],"regular":[142],"semi-regular":[144],"classified.":[152]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
