{"id":"https://openalex.org/W1994454756","doi":"https://doi.org/10.1002/jgt.3190190310","title":"The edge reconstruction number of a disconnected graph","display_name":"The edge reconstruction number of a disconnected graph","publication_year":1995,"publication_date":"1995-05-01","ids":{"openalex":"https://openalex.org/W1994454756","doi":"https://doi.org/10.1002/jgt.3190190310","mag":"1994454756"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190190310","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190190310","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","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/A5002646314","display_name":"Robert Molina","orcid":null},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert Molina","raw_affiliation_strings":["Department of Mathematics Colorado State University Fort Collins, Colorado","DEPARTMENT OF MATHEMATICS, COLORADO STATE UNIVERSITY, FORT COLLINS, COLORADO"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Colorado State University Fort Collins, Colorado","institution_ids":["https://openalex.org/I92446798"]},{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS, COLORADO STATE UNIVERSITY, FORT COLLINS, COLORADO","institution_ids":["https://openalex.org/I92446798"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002646314"],"corresponding_institution_ids":["https://openalex.org/I92446798"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.12125576,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"19","issue":"3","first_page":"375","last_page":"384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980000257492065,"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":0.9980000257492065,"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":0.9951000213623047,"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":0.9921000003814697,"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":0.8433182239532471},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8290300965309143},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5775228142738342},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5673762559890747},{"id":"https://openalex.org/keywords/edge-transitive-graph","display_name":"Edge-transitive graph","score":0.47795534133911133},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.47385361790657043},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45717909932136536},{"id":"https://openalex.org/keywords/complement-graph","display_name":"Complement graph","score":0.4168775677680969},{"id":"https://openalex.org/keywords/totally-disconnected-space","display_name":"Totally disconnected space","score":0.4156688451766968},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.3619094491004944},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.33487996459007263}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8433182239532471},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8290300965309143},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5775228142738342},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5673762559890747},{"id":"https://openalex.org/C200597783","wikidata":"https://www.wikidata.org/wiki/Q4391289","display_name":"Edge-transitive graph","level":5,"score":0.47795534133911133},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.47385361790657043},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45717909932136536},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.4168775677680969},{"id":"https://openalex.org/C89436406","wikidata":"https://www.wikidata.org/wiki/Q1544261","display_name":"Totally disconnected space","level":3,"score":0.4156688451766968},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.3619094491004944},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.33487996459007263},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/jgt.3190190310","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190190310","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.553.3938","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.553.3938","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://othello.alma.edu/~molina/papers/pdf papers/RN(D).pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2075084424","https://openalex.org/W2098123445"],"related_works":["https://openalex.org/W2380035736","https://openalex.org/W4298172984","https://openalex.org/W3193236920","https://openalex.org/W4213419526","https://openalex.org/W2391570583","https://openalex.org/W3037602378","https://openalex.org/W2040301912","https://openalex.org/W2103478523","https://openalex.org/W2358075237","https://openalex.org/W2167092525"],"abstract_inverted_index":{"Abstract":[0],"The":[1,105],"edge":[2,16,106,144],"reconstruction":[3,107,117,145,157],"number":[4,14,146,158],"of":[5,15,47,60,89,125,147,159],"a":[6,32,45,58,66,70,94,126,138,148,160],"graph":[7,34,95,150,161],"G,":[8],"RN(G)":[9,52,81,100],",":[10,131],"is":[11,64,141,151,162],"the":[12,28,115,143,155],"minimum":[13],"deleted":[17],"subgraphs":[18],"required":[19],"to":[20,24,93,114],"determine":[21],"G":[22,35,43,56,90],"up":[23],"isomorphism.":[25],"We":[26],"prove":[27],"following":[29],"results":[30,108,118],"for":[31],"disconnected":[33,149],"with":[36,96],"at":[37],"least":[38],"two":[39],"nontrivial":[40,48,61,71,87],"components.":[41],"If":[42,55],"has":[44,57],"pair":[46,59],"nonisomorphic":[49,62],"components":[50,88],"then":[51,80,99],"\u2264":[53,82,101],"3.":[54],"components,":[63],"not":[65],"forest,":[67],"and":[68],"contains":[69],"component":[72],"other":[73],"than":[74],"K":[75,78],"3":[76],"or":[77,165],"1,3":[79],"2.":[83,104],"Finally,":[84],"if":[85],"all":[86],"are":[91,112],"isomorphic":[92],"k":[97,102],"edges,":[98],"+":[103],"in":[109],"this":[110],"paper":[111],"similar":[113],"vertex":[116,156],"stated":[119],"by":[120],"Myrvold":[121],"(\u201cThe":[122],"Ally\u2010Reconstruction":[123],"Number":[124],"Disconnected":[127],"Graph,\u201d":[128],"Ars":[129],"Combinatoria":[130],"Vol.":[132],"28":[133],"[1989]":[134],"pp.":[135],"123\u2010127),":[136],"but":[137],"significant":[139],"difference":[140],"that":[142],"often":[152],"two,":[153],"while":[154],"always":[163],"three":[164],"more.":[166],"\u00a9":[167],"1995":[168],"John":[169],"Wiley":[170],"&amp;":[171],"Sons,":[172],"Inc.":[173]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
