{"id":"https://openalex.org/W2044262022","doi":"https://doi.org/10.1142/s0219265909002522","title":"BOUNDS ON THE DOMINATION NUMBER OF PERMUTATION GRAPHS","display_name":"BOUNDS ON THE DOMINATION NUMBER OF PERMUTATION GRAPHS","publication_year":2009,"publication_date":"2009-09-01","ids":{"openalex":"https://openalex.org/W2044262022","doi":"https://doi.org/10.1142/s0219265909002522","mag":"2044262022"},"language":"en","primary_location":{"id":"doi:10.1142/s0219265909002522","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219265909002522","pdf_url":null,"source":{"id":"https://openalex.org/S63112013","display_name":"Journal of Interconnection Networks","issn_l":"0219-2659","issn":["0219-2659","1793-6713"],"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":"Journal of Interconnection Networks","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/A5100859141","display_name":"Weizhen Gu","orcid":null},"institutions":[{"id":"https://openalex.org/I13511017","display_name":"Texas State University","ror":"https://ror.org/05h9q1g27","country_code":"US","type":"education","lineage":["https://openalex.org/I13511017"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"WEIZHEN GU","raw_affiliation_strings":["Mathematics Department, Texas State University, 601 University Drive, San Marcos, TX 78666, USA"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Texas State University, 601 University Drive, San Marcos, TX 78666, USA","institution_ids":["https://openalex.org/I13511017"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018001470","display_name":"Kirsti Wash","orcid":null},"institutions":[{"id":"https://openalex.org/I13511017","display_name":"Texas State University","ror":"https://ror.org/05h9q1g27","country_code":"US","type":"education","lineage":["https://openalex.org/I13511017"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"KIRSTI WASH","raw_affiliation_strings":["Mathematics Department, Texas State University, 601 University Drive, San Marcos, TX 78666, USA"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Texas State University, 601 University Drive, San Marcos, TX 78666, USA","institution_ids":["https://openalex.org/I13511017"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100859141"],"corresponding_institution_ids":["https://openalex.org/I13511017"],"apc_list":null,"apc_paid":null,"fwci":0.3428,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.60236601,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"10","issue":"03","first_page":"205","last_page":"217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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":0.9997000098228455,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9987999796867371,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9789999723434448,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8855646848678589},{"id":"https://openalex.org/keywords/permutation-graph","display_name":"Permutation graph","score":0.7145060896873474},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.665631115436554},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.5387827157974243},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5353325605392456},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.5000302791595459},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4988672733306885},{"id":"https://openalex.org/keywords/cyclic-permutation","display_name":"Cyclic permutation","score":0.490181028842926},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.2936922609806061},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.16362375020980835},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0718165934085846}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8855646848678589},{"id":"https://openalex.org/C68965932","wikidata":"https://www.wikidata.org/wiki/Q7169369","display_name":"Permutation graph","level":3,"score":0.7145060896873474},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.665631115436554},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.5387827157974243},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5353325605392456},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5000302791595459},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4988672733306885},{"id":"https://openalex.org/C77670614","wikidata":"https://www.wikidata.org/wiki/Q212130","display_name":"Cyclic permutation","level":3,"score":0.490181028842926},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.2936922609806061},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.16362375020980835},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0718165934085846},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219265909002522","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219265909002522","pdf_url":null,"source":{"id":"https://openalex.org/S63112013","display_name":"Journal of Interconnection Networks","issn_l":"0219-2659","issn":["0219-2659","1793-6713"],"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":"Journal of Interconnection Networks","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":10,"referenced_works":["https://openalex.org/W359573505","https://openalex.org/W855674090","https://openalex.org/W1493071618","https://openalex.org/W1968949736","https://openalex.org/W1969337449","https://openalex.org/W1979487908","https://openalex.org/W2008194433","https://openalex.org/W2157516444","https://openalex.org/W3106990226","https://openalex.org/W3141776272"],"related_works":["https://openalex.org/W2385551783","https://openalex.org/W2964309395","https://openalex.org/W4285292213","https://openalex.org/W2356795487","https://openalex.org/W2952662568","https://openalex.org/W2141765721","https://openalex.org/W2391050754","https://openalex.org/W3133549692","https://openalex.org/W2349665798","https://openalex.org/W2078652738"],"abstract_inverted_index":{"For":[0],"a":[1,8,13,47,79,106,133,145,149,158],"graph":[2,15,48,118,135],"G":[3,26,96,136],"with":[4,148],"n":[5],"vertices":[6],"and":[7,33,137,146,159],"permutation":[9,14,64,80,117,138],"\u03b1":[10,17,58,65,81,85,139,161],"on":[11,66],"V(G),":[12],"P":[16],"(G)":[18,59],"is":[19,119],"obtained":[20],"from":[21],"two":[22,142],"identical":[23],"copies":[24],"of":[25,46,91,95,101,108,115,124],"by":[27],"adding":[28],"an":[29],"edge":[30],"between":[31],"v":[32,37],"\u03b1(V)":[34],"for":[35,62,75,110,140],"any":[36,63,116,141],"\u03f5":[38],"V(G).":[39,67],"Let":[40],"\u03b3(G)":[41,55,88,156],"be":[42],"the":[43,92,98,112,121,125],"domination":[44,93,113,122],"number":[45,94,114,123],"G.":[49,102],"It":[50],"has":[51],"been":[52],"shown":[53],"that":[54,83],"\u2264":[56,60,150,152],"\u03b3(P":[57,84,160],"2\u03b3(G)":[61],"In":[68],"this":[69],"paper,":[70],"we":[71,104],"investigate":[72],"specific":[73,134],"graphs":[74,109],"which":[76,111],"there":[77],"exists":[78],"such":[82],"(G))":[86,162],"\u227b":[87],"in":[89],"terms":[90],"or":[97],"maximum":[99],"degree":[100],"Additionally,":[103],"construct":[105],"class":[107],"twice":[120],"original":[126],"graph,":[127],"as":[128,130],"well":[129],"explore":[131],"finding":[132],"positive":[143],"integers":[144],"b":[147,151],"2a,":[153],"to":[154],"have":[155],"=":[157,163],"b.":[164]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
