{"id":"https://openalex.org/W2121373282","doi":"https://doi.org/10.1002/jgt.3190010407","title":"The number of connected sparsely edged graphs","display_name":"The number of connected sparsely edged graphs","publication_year":1977,"publication_date":"1977-12-01","ids":{"openalex":"https://openalex.org/W2121373282","doi":"https://doi.org/10.1002/jgt.3190010407","mag":"2121373282"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190010407","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190010407","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/A5113446114","display_name":"E. M. Wright","orcid":null},"institutions":[{"id":"https://openalex.org/I195460627","display_name":"University of Aberdeen","ror":"https://ror.org/016476m91","country_code":"GB","type":"education","lineage":["https://openalex.org/I195460627"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"E. M. Wright","raw_affiliation_strings":["University of Aberdeen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Aberdeen","institution_ids":["https://openalex.org/I195460627"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5113446114"],"corresponding_institution_ids":["https://openalex.org/I195460627"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":1.8534,"has_fulltext":false,"cited_by_count":151,"citation_normalized_percentile":{"value":0.87609329,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"1","issue":"4","first_page":"317","last_page":"330"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9994000196456909,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9984999895095825,"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/T11269","display_name":"Algorithms and Data Compression","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mathematics","display_name":"Mathematics","score":0.832768976688385},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.823127031326294},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.5995876789093018},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5278463363647461},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4923957586288452},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4886327385902405},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.45140963792800903},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4503194987773895},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.43575379252433777},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.423860639333725},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09751957654953003}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.832768976688385},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.823127031326294},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.5995876789093018},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5278463363647461},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4923957586288452},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4886327385902405},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.45140963792800903},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4503194987773895},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.43575379252433777},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.423860639333725},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09751957654953003},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190010407","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190010407","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1981070879","https://openalex.org/W2616697817","https://openalex.org/W4213214460","https://openalex.org/W6738002306","https://openalex.org/W7052736799"],"related_works":["https://openalex.org/W2320114089","https://openalex.org/W2066808294","https://openalex.org/W4226275486","https://openalex.org/W2021255209","https://openalex.org/W1571832314","https://openalex.org/W2084488871","https://openalex.org/W4298259995","https://openalex.org/W1525332241","https://openalex.org/W2006638646","https://openalex.org/W4286751119"],"abstract_inverted_index":{"Abstract":[0],"An":[1],"(":[2,23],"n,":[3,24],"q":[4,11,25],")":[5,26,38],"graph":[6],"has":[7],"n":[8,36,40,64,78],"labeled":[9],"points,":[10],"edges,":[12],"and":[13,42,70,95,123,149],"no":[14],"loops":[15],"or":[16,132],"multiple":[17],"edges.":[18],"The":[19,84,115],"number":[20],"of":[21,62,145,167],"connected":[22],"graphs":[27],"is":[28,87,96,119,124,144],"f(n,":[29,35,48,63,77],"q)":[30],".":[31,50],"Cayley":[32],"proved":[33],"that":[34,109,140,151],"\u20101":[37],"=":[39],"n\u22122":[41],"Renyi":[43],"found":[44],"a":[45,74,88,107,146],"formula":[46,75],"for":[47,67,76,81,99,127,158],"n)":[49],"Here":[51],"I":[52],"develop":[53],"two":[54],"methods":[55],"to":[56,72,93,164],"calculate":[57],"the":[58,137,141,152,165,168],"exponential":[59],"generating":[60,142],"function":[61,143],"+":[65,79],"k)":[66,80],"particular":[68,147],"k":[69,94,128,160],"so":[71,150],"find":[73],"general":[82],"n.":[83],"first":[85,153],"method":[86,118,154],"recurrent":[89],"one":[90],"with":[91],"respect":[92],"well":[97],"adapted":[98],"machine":[100],"computation,":[101],"but":[102,134],"does":[103],"not":[104],"itself":[105],"provide":[106],"proof":[108,139],"it":[110,135],"can":[111,155],"be":[112,156],"continued":[113,157],"indefinitely.":[114],"second":[116],"(reduction)":[117],"much":[120],"less":[121],"efficient":[122],"indeed":[125],"impracticable":[126],"greater":[129],"than":[130],"2":[131],"3,":[133],"supplies":[136],"missing":[138],"form":[148],"all":[159],",":[161],"subject":[162],"only":[163],"capacity":[166],"machine.":[169]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":6}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}