{"id":"https://openalex.org/W2086566679","doi":"https://doi.org/10.1109/icnc.2013.6818271","title":"Counting the number of spanning trees of generalization Farey graph","display_name":"Counting the number of spanning trees of generalization Farey graph","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W2086566679","doi":"https://doi.org/10.1109/icnc.2013.6818271","mag":"2086566679"},"language":"en","primary_location":{"id":"doi:10.1109/icnc.2013.6818271","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icnc.2013.6818271","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 Ninth International Conference on Natural Computation (ICNC)","raw_type":"proceedings-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/A5023270649","display_name":"Yuzhi Xiao","orcid":"https://orcid.org/0000-0003-2086-0422"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuzhi Xiao","raw_affiliation_strings":["School of Computer Science, ShaanXi Normal University, Xi'an, ShaanXi, P. R. China","School of Computer Science, ShaanXi Normal University, Xi'an, ShaanXi, 710062, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, ShaanXi Normal University, Xi'an, ShaanXi, P. R. China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"School of Computer Science, ShaanXi Normal University, Xi'an, ShaanXi, 710062, P. R. China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078200110","display_name":"Haixing Zhao","orcid":"https://orcid.org/0000-0003-0957-1603"},"institutions":[{"id":"https://openalex.org/I20616075","display_name":"Qinghai Normal University","ror":"https://ror.org/03az1t892","country_code":"CN","type":"education","lineage":["https://openalex.org/I20616075"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haixing Zhao","raw_affiliation_strings":["School of Computer, Qinghai Normal University, Xining, Qinghai, P. R. China","School of Computer, Qinghai Normal University, Xining, Qinghai, 810008, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Computer, Qinghai Normal University, Xining, Qinghai, P. R. China","institution_ids":["https://openalex.org/I20616075"]},{"raw_affiliation_string":"School of Computer, Qinghai Normal University, Xining, Qinghai, 810008, P. R. China","institution_ids":["https://openalex.org/I20616075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023270649"],"corresponding_institution_ids":["https://openalex.org/I88830068"],"apc_list":null,"apc_paid":null,"fwci":0.9294,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.74920117,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1778","last_page":"1782"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9950000047683716,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/spanning-tree","display_name":"Spanning tree","score":0.887671947479248},{"id":"https://openalex.org/keywords/farey-sequence","display_name":"Farey sequence","score":0.824169397354126},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7158511281013489},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.641577422618866},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5635508298873901},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5416515469551086},{"id":"https://openalex.org/keywords/tr\u00e9maux-tree","display_name":"Tr\u00e9maux tree","score":0.5024843215942383},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.462873250246048},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.46062153577804565},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.43562835454940796},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.22318968176841736},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.06771621108055115}],"concepts":[{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.887671947479248},{"id":"https://openalex.org/C93157843","wikidata":"https://www.wikidata.org/wiki/Q1396592","display_name":"Farey sequence","level":2,"score":0.824169397354126},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7158511281013489},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.641577422618866},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5635508298873901},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5416515469551086},{"id":"https://openalex.org/C124302570","wikidata":"https://www.wikidata.org/wiki/Q7849146","display_name":"Tr\u00e9maux tree","level":5,"score":0.5024843215942383},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.462873250246048},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.46062153577804565},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.43562835454940796},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.22318968176841736},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.06771621108055115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icnc.2013.6818271","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icnc.2013.6818271","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 Ninth International Conference on Natural Computation (ICNC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1965922183","https://openalex.org/W1975001554","https://openalex.org/W1992346289","https://openalex.org/W1995519784","https://openalex.org/W1997371824","https://openalex.org/W2001149343","https://openalex.org/W2018418637","https://openalex.org/W2019932401","https://openalex.org/W2022322758","https://openalex.org/W2029673229","https://openalex.org/W2037685751","https://openalex.org/W2040574334","https://openalex.org/W2050370193","https://openalex.org/W2055159727","https://openalex.org/W2061309095","https://openalex.org/W2069680987","https://openalex.org/W2086320116","https://openalex.org/W2092153036","https://openalex.org/W2121699196","https://openalex.org/W2144873820","https://openalex.org/W2166982528","https://openalex.org/W3101221984","https://openalex.org/W4234361933"],"related_works":["https://openalex.org/W4231397933","https://openalex.org/W2374925474","https://openalex.org/W2911818503","https://openalex.org/W2779618893","https://openalex.org/W4380840098","https://openalex.org/W1966931974","https://openalex.org/W2138987445","https://openalex.org/W1541890612","https://openalex.org/W1570182137","https://openalex.org/W1738503018"],"abstract_inverted_index":{"Spanning":[0],"trees":[1,19,38,85,144,163],"are":[2],"an":[3,45],"important":[4],"quantity":[5],"characterizing":[6],"the":[7,15,34,62,68,73,80,87,94,105,118,140,156,170],"reliability":[8],"of":[9,17,36,48,83,104,120,127,142,145,161,164,167],"a":[10,23,31,40,124,133],"network,":[11,146],"however,":[12],"explicitly":[13],"determining":[14],"number":[16,82,119,141],"spanning":[18,37,84,143,162],"in":[20,39,86],"networks":[21,168],"is":[22,52,59,97,100,117,137],"theoretical":[24],"challenge.":[25],"In":[26],"this":[27],"paper,":[28],"we":[29,78],"perform":[30],"study":[32],"on":[33],"enumeration":[35],"specific":[41],"small-world":[42],"network":[43,70],"with":[44,61,109,150],"exponential":[46],"distribution":[47],"vertex":[49],"degrees,":[50],"which":[51,99,136,147],"called":[53],"generalization":[54,128],"Farey":[55,64,88,129],"graph":[56,130],"since":[57],"it":[58],"associated":[60],"famous":[63],"sequence.":[65],"According":[66],"to":[67,139],"particular":[69],"structure,":[71],"use":[72],"method,":[74],"proposed":[75],"by":[76,132],"us,":[77],"obtain":[79,155],"exact":[81],"graph.":[89],"The":[90],"result":[91],"shows":[92],"that":[93,103],"computation":[95],"complexity":[96],"O(n),":[98],"better":[101],"than":[102],"matrix":[106],"tree":[107],"theorem":[108],"O(n":[110],"<sup":[111],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[112],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[113],"),":[114],"where":[115],"n":[116],"steps.":[121],"We":[122,153],"derive":[123],"basic":[125],"property":[126],"controlled":[131],"parameter":[134],"k,":[135],"closely":[138],"become":[148],"bigger":[149],"increasing":[151],"k.":[152],"also":[154],"maximum":[157],"and":[158],"minimum":[159],"numbers":[160],"these":[165],"kinds":[166],"through":[169],"method.":[171]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}