{"id":"https://openalex.org/W4283749195","doi":"https://doi.org/10.1080/09728600.2022.2077674","title":"Truly non-trivial graphoidal graphs","display_name":"Truly non-trivial graphoidal graphs","publication_year":2022,"publication_date":"2022-05-04","ids":{"openalex":"https://openalex.org/W4283749195","doi":"https://doi.org/10.1080/09728600.2022.2077674"},"language":"en","primary_location":{"id":"doi:10.1080/09728600.2022.2077674","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2022.2077674","pdf_url":null,"source":{"id":"https://openalex.org/S2764899362","display_name":"AKCE International Journal of Graphs and Combinatorics","issn_l":"0972-8600","issn":["0972-8600","2543-3474"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1080/09728600.2022.2077674","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024994848","display_name":"Rajesh Singh","orcid":"https://orcid.org/0000-0002-2184-8655"},"institutions":[{"id":"https://openalex.org/I110166357","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213","country_code":"IN","type":"education","lineage":["https://openalex.org/I110166357"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Rajesh Singh","raw_affiliation_strings":["Department of Mathematics, Ramanujan College, University of Delhi, Delhi, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ramanujan College, University of Delhi, Delhi, India","institution_ids":["https://openalex.org/I110166357"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008708299","display_name":"Purnima Gupta","orcid":"https://orcid.org/0000-0003-4389-3024"},"institutions":[{"id":"https://openalex.org/I110166357","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213","country_code":"IN","type":"education","lineage":["https://openalex.org/I110166357"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Purnima Gupta","raw_affiliation_strings":["Department of Mathematics, Sri Venkateswara College, University of Delhi, Delhi, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sri Venkateswara College, University of Delhi, Delhi, India","institution_ids":["https://openalex.org/I110166357"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043658441","display_name":"S. Arumugam","orcid":"https://orcid.org/0000-0002-4477-9453"},"institutions":[{"id":"https://openalex.org/I98499257","display_name":"Kalasalingam Academy of Research and Education","ror":"https://ror.org/04fm2fn75","country_code":"IN","type":"education","lineage":["https://openalex.org/I98499257"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"S. Arumugam","raw_affiliation_strings":["National Centre for Advanced Research in Discrete Mathematics, Kalasalingam University, Krishnankoil, Tamil Nadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Centre for Advanced Research in Discrete Mathematics, Kalasalingam University, Krishnankoil, Tamil Nadu, India","institution_ids":["https://openalex.org/I98499257"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024994848"],"corresponding_institution_ids":["https://openalex.org/I110166357"],"apc_list":{"value":1000,"currency":"GBP","value_usd":1226},"apc_paid":{"value":1000,"currency":"GBP","value_usd":1226},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09825112,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"2","first_page":"112","last_page":"117"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9970999956130981,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9965000152587891,"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/combinatorics","display_name":"Combinatorics","score":0.8164639472961426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7136890888214111},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.679764986038208},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.6121269464492798},{"id":"https://openalex.org/keywords/edge-cover","display_name":"Edge cover","score":0.5470165610313416},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5321171879768372},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.5193991661071777},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5064111948013306},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.44467851519584656},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4361311197280884},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17168262600898743}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8164639472961426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7136890888214111},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.679764986038208},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.6121269464492798},{"id":"https://openalex.org/C17762858","wikidata":"https://www.wikidata.org/wiki/Q594001","display_name":"Edge cover","level":3,"score":0.5470165610313416},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5321171879768372},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.5193991661071777},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5064111948013306},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.44467851519584656},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4361311197280884},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17168262600898743},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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":2,"locations":[{"id":"doi:10.1080/09728600.2022.2077674","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2022.2077674","pdf_url":null,"source":{"id":"https://openalex.org/S2764899362","display_name":"AKCE International Journal of Graphs and Combinatorics","issn_l":"0972-8600","issn":["0972-8600","2543-3474"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:890c96b0d4a543eab5aee59ea8c00c66","is_oa":true,"landing_page_url":"https://doaj.org/article/890c96b0d4a543eab5aee59ea8c00c66","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":"AKCE International Journal of Graphs and Combinatorics, Vol 19, Iss 2, Pp 112-117 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1080/09728600.2022.2077674","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2022.2077674","pdf_url":null,"source":{"id":"https://openalex.org/S2764899362","display_name":"AKCE International Journal of Graphs and Combinatorics","issn_l":"0972-8600","issn":["0972-8600","2543-3474"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1974811277","https://openalex.org/W1976489861","https://openalex.org/W1988932681","https://openalex.org/W1993102073","https://openalex.org/W1993412054","https://openalex.org/W2006621708","https://openalex.org/W2021962931","https://openalex.org/W2028032378","https://openalex.org/W2036751548","https://openalex.org/W2047960318","https://openalex.org/W2063733383","https://openalex.org/W4213214460"],"related_works":["https://openalex.org/W2949255922","https://openalex.org/W2036594069","https://openalex.org/W4244658307","https://openalex.org/W2156896570","https://openalex.org/W2038655901","https://openalex.org/W1627181101","https://openalex.org/W2043560626","https://openalex.org/W1558145674","https://openalex.org/W9203110","https://openalex.org/W2379188955"],"abstract_inverted_index":{"A":[0],"graphoidal":[1,61,74,84,87,107,146,170,179,190],"cover":[2,75,85,180],"of":[3,13,27,33,45,65,89,120,135,152],"a":[4,8,60,81,101,105,130,140,144,189],"graph":[5,66,102,141,186],"G":[6,28,46,67],"is":[7,29,47,79],"collection":[9],"[Formula:":[10,39,53,62,76,124,165],"see":[11,40,54,63,77,125,166],"text]":[12,41,55,64,78,126,167],"non-trivial":[14,83],"paths":[15],"in":[16,38,48,52,59,117,133],"G,":[17],"which":[18],"are":[19,115],"not":[20],"necessarily":[21],"open,":[22],"such":[23,188],"that":[24,112,183],"every":[25,43,57,184],"vertex":[26,32],"an":[30,150],"internal":[31],"at":[34,70],"most":[35],"one":[36,50],"path":[37,51,58],"and":[42,137,161,181],"edge":[44],"exactly":[49],"If":[56],"has":[68],"length":[69],"least":[71],"2,":[72],"then":[73],"called":[80],"truly":[82],"(TNT":[86],"cover)":[88],"G.":[90],"In":[91],"this":[92],"paper":[93],"we":[94,156,173],"obtain":[95,129],"some":[96],"structural":[97],"necessary":[98,131,154],"conditions":[99,114],"for":[100,139],"to":[103,142],"possess":[104,143],"TNT":[106,145,169,178],"cover.":[108,147,171,191],"We":[109,127],"also":[110,128],"exhibit":[111],"these":[113],"sufficient":[116],"the":[118,153],"case":[119],"trees":[121],"with":[122],"diameter":[123],"condition":[132],"terms":[134],"order":[136],"size":[138],"Thereafter":[148],"as":[149],"application":[151],"condition,":[155],"characterize":[157],"complete":[158,162],"graphs":[159,164,176],"Kn":[160],"bipartite":[163],"possessing":[168,177],"Finally,":[172],"discuss":[174],"regular":[175],"prove":[182],"3-regular":[185],"possesses":[187]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
