{"id":"https://openalex.org/W2056914622","doi":"https://doi.org/10.1002/jgt.3190020403","title":"The number of connected sparsely edged graphs. II. Smooth graphs and blocks","display_name":"The number of connected sparsely edged graphs. II. Smooth graphs and blocks","publication_year":1978,"publication_date":"1978-12-01","ids":{"openalex":"https://openalex.org/W2056914622","doi":"https://doi.org/10.1002/jgt.3190020403","mag":"2056914622"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190020403","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190020403","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/A5037377329","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/A5037377329"],"corresponding_institution_ids":["https://openalex.org/I195460627"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":1.3649,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.80794702,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2","issue":"4","first_page":"299","last_page":"305"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998999834060669,"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/T11329","display_name":"Limits and Structures in Graph Theory","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/T10374","display_name":"Advanced Graph Theory Research","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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8611063957214355},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8152858018875122},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5423276424407959},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47965434193611145}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8611063957214355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8152858018875122},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5423276424407959},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47965434193611145}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190020403","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190020403","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":[{"id":"https://openalex.org/F4320332447","display_name":"U.S. Army","ror":"https://ror.org/00afsp483"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1970351638","https://openalex.org/W2016317209","https://openalex.org/W2121373282"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2142036596"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"smooth":[2,30],"graph":[3,7],"is":[4,15,26,38],"a":[5,134,150],"connected":[6,19],"without":[8],"endpoints;":[9],"f":[10,65],"(":[11,22,34,66,73,81,167,175],"n,":[12,23,35,67,74,82,168,176],"q":[13,24,36,48],")":[14,25,37,172,180],"the":[16,27,39,60,116,125],"number":[17,28,40],"of":[18,29,41,64,136,140],"graphs,":[20,31],"v":[21,72,166],"and":[32,47,56,79,173],"u":[33,80,174],"blocks":[42],"on":[43],"n":[44,68,75,83,169,177,183],"labeled":[45],"points":[46],"edges:":[49],"W":[50,106],"k":[51,54,58,70,77,85,90,99,107,114,131,158,161,171,179],",":[52,55,108],"V":[53,98],"U":[57,130,157],"are":[59],"exponential":[61],"generating":[62],"functions":[63],"+":[69,76,84,170,178],"),":[71,78,86],"respectively.":[87],"For":[88],"any":[89],"\u2a7e":[91],"1,":[92],"our":[93,121],"reduction":[94,126],"method":[95,118,127,152],"shows":[96,128],"that":[97,129],"can":[100],"be":[101,133],"deduced":[102],"at":[103,185],"once":[104],"from":[105],"which":[109],"was":[110],"found":[111],"for":[112,159,165,181],"successive":[113,160],"by":[115],"computer":[117],"described":[119],"in":[120],"previous":[122],"paper.":[123],"Again":[124],"must":[132],"sum":[135],"powers":[137],"(mostly":[138],"negative)":[139],"1":[141],"\u2010":[142],"X":[143],"and,":[144],"given":[145],"this":[146],"information,":[147],"we":[148],"develop":[149],"recurrence":[151],"well":[153],"suited":[154],"to":[155],"calculate":[156],".":[162],"Exact":[163],"formulas":[164],"general":[182],"follow":[184],"once.":[186]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}