{"id":"https://openalex.org/W2757558283","doi":"https://doi.org/10.1142/s1793830917500677","title":"Graphs with cyclomatic number three having panconnected square","display_name":"Graphs with cyclomatic number three having panconnected square","publication_year":2017,"publication_date":"2017-09-28","ids":{"openalex":"https://openalex.org/W2757558283","doi":"https://doi.org/10.1142/s1793830917500677","mag":"2757558283"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830917500677","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830917500677","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/A5112502219","display_name":"Gek L. Chia","orcid":null},"institutions":[{"id":"https://openalex.org/I931681460","display_name":"Universiti Tunku Abdul Rahman","ror":"https://ror.org/050pq4m56","country_code":"MY","type":"education","lineage":["https://openalex.org/I931681460"]},{"id":"https://openalex.org/I33849332","display_name":"University of Malaya","ror":"https://ror.org/00rzspn62","country_code":"MY","type":"education","lineage":["https://openalex.org/I33849332"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"G. L. Chia","raw_affiliation_strings":["Department of Mathematical and Actuarial Sciences, Universiti Tunku Abdul Rahman, Sungai Long, Malaysia","Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Actuarial Sciences, Universiti Tunku Abdul Rahman, Sungai Long, Malaysia","institution_ids":["https://openalex.org/I931681460"]},{"raw_affiliation_string":"Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia","institution_ids":["https://openalex.org/I33849332"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005418374","display_name":"W. Hemakul","orcid":null},"institutions":[{"id":"https://openalex.org/I158708052","display_name":"Chulalongkorn University","ror":"https://ror.org/028wp3y58","country_code":"TH","type":"education","lineage":["https://openalex.org/I158708052"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"W. Hemakul","raw_affiliation_strings":["Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand","institution_ids":["https://openalex.org/I158708052"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086610178","display_name":"Sirirat Singhun","orcid":"https://orcid.org/0000-0002-2519-9701"},"institutions":[{"id":"https://openalex.org/I4210117768","display_name":"Centre of Excellence in Mathematics","ror":"https://ror.org/02df7gw66","country_code":"TH","type":"education","lineage":["https://openalex.org/I4210117768"]},{"id":"https://openalex.org/I58196637","display_name":"Ramkhamhaeng University","ror":"https://ror.org/00mrw8k38","country_code":"TH","type":"education","lineage":["https://openalex.org/I58196637"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"S. Singhun","raw_affiliation_strings":["Centre of Excellence in Mathematics, CHE, Si Ayuthaya Rd., Bangkok 10400, Thailand","Department of Mathematics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand"],"affiliations":[{"raw_affiliation_string":"Centre of Excellence in Mathematics, CHE, Si Ayuthaya Rd., Bangkok 10400, Thailand","institution_ids":["https://openalex.org/I4210117768"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand","institution_ids":["https://openalex.org/I58196637"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5112502219"],"corresponding_institution_ids":["https://openalex.org/I33849332","https://openalex.org/I931681460"],"apc_list":null,"apc_paid":null,"fwci":0.2271,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.56357149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"09","issue":"05","first_page":"1750067","last_page":"1750067"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9937000274658203,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9937000274658203,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9930999875068665,"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/T11476","display_name":"Graph theory and applications","score":0.9926999807357788,"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":0.683127224445343},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6060964465141296},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.5670216083526611},{"id":"https://openalex.org/keywords/cyclomatic-complexity","display_name":"Cyclomatic complexity","score":0.5435379147529602},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5368868112564087},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4962018132209778},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1599014699459076}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.683127224445343},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6060964465141296},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5670216083526611},{"id":"https://openalex.org/C187303228","wikidata":"https://www.wikidata.org/wiki/Q867330","display_name":"Cyclomatic complexity","level":3,"score":0.5435379147529602},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5368868112564087},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4962018132209778},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1599014699459076},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830917500677","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830917500677","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":6,"referenced_works":["https://openalex.org/W1989780696","https://openalex.org/W2002687070","https://openalex.org/W2016126876","https://openalex.org/W2017108431","https://openalex.org/W2028535821","https://openalex.org/W2045633145"],"related_works":["https://openalex.org/W2351691141","https://openalex.org/W4287862836","https://openalex.org/W3008482400","https://openalex.org/W2242288932","https://openalex.org/W1517065984","https://openalex.org/W2993717413","https://openalex.org/W2148423957","https://openalex.org/W2079697429","https://openalex.org/W1969211012","https://openalex.org/W2002687070"],"abstract_inverted_index":{"The":[0],"square":[1,66,89,181],"of":[2,22,45,146,150,170],"a":[3],"graph":[4,10],"[Formula:":[5,13,30,36,46,52,62,125,131,135,141,152,174],"see":[6,14,31,37,47,53,63,126,132,136,142,153,175],"text]":[7,15,32,38,48,64,127,133,137,143,176],"is":[8,33,39,49,138,144],"the":[9,42,147,157],"obtained":[11],"from":[12,26],"by":[16],"adding":[17],"edges":[18],"joining":[19],"those":[20],"pairs":[21],"vertices":[23],"whose":[24,65,88,180],"distance":[25],"each":[27],"other":[28,73],"in":[29,75,156],"two.":[34],"If":[35],"connected,":[40],"then":[41,140],"cyclomatic":[43,57,109,129],"number":[44,58,110,130],"defined":[50,155],"as":[51,177],"text].":[54],"Graphs":[55,107],"with":[56,108],"not":[59],"more":[60],"than":[61],"are":[67,182],"panconnected":[68,113],"have":[69,90],"been":[70],"characterized,":[71],"among":[72],"things,":[74],"[G.":[76],"L.":[77,83,100],"Chia,":[78,101],"S.":[79,105],"H.":[80],"Ong":[81],"and":[82,104,134,163],"Y.":[84],"Tan,":[85],"On":[86],"graphs":[87,171],"strong":[91],"Hamiltonian":[92],"properties,":[93],"Discrete":[94,115],"Math.":[95,116],"309":[96],"(2009)":[97],"4608\u20134613,":[98],"G.":[99],"W.":[102],"Hemakul":[103],"Singhun,":[106],"two":[111],"having":[112],"square,":[114],"311":[117],"(2011)":[118],"850\u2013855].":[119],"Here,":[120],"we":[121,160],"show":[122],"that":[123],"if":[124],"has":[128],"panconnected,":[139],"one":[145],"eight":[148],"families":[149,169],"graphs,":[151],"text],":[154],"paper.":[158],"Further,":[159],"obtain":[161],"necessary":[162],"sufficient":[164],"conditions":[165],"for":[166],"three":[167],"larger":[168],"(which":[172],"contains":[173],"special":[178],"cases)":[179],"panconnected.":[183]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}