{"id":"https://openalex.org/W2966452567","doi":"https://doi.org/10.1109/access.2019.2931406","title":"Resistance Distance and Kirchhoff Index of $Q$ -Double Join Graphs","display_name":"Resistance Distance and Kirchhoff Index of $Q$ -Double Join Graphs","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2966452567","doi":"https://doi.org/10.1109/access.2019.2931406","mag":"2966452567"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2931406","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2931406","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08777072.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08777072.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101418559","display_name":"Weizhong Wang","orcid":"https://orcid.org/0009-0000-9891-6516"},"institutions":[{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Weizhong Wang","raw_affiliation_strings":["School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, China","institution_ids":["https://openalex.org/I3133134087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042047960","display_name":"Tingyan Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tingyan Ma","raw_affiliation_strings":["School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, China","institution_ids":["https://openalex.org/I3133134087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076981458","display_name":"Jia\u2010Bao Liu","orcid":"https://orcid.org/0000-0002-9620-7692"},"institutions":[{"id":"https://openalex.org/I118987531","display_name":"Anhui Jianzhu University","ror":"https://ror.org/0108wjw08","country_code":"CN","type":"education","lineage":["https://openalex.org/I118987531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jia-Bao Liu","raw_affiliation_strings":["School of Mathematics and Physics, Anhui Jianzhu University, Hefei, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Anhui Jianzhu University, Hefei, China","institution_ids":["https://openalex.org/I118987531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101418559"],"corresponding_institution_ids":["https://openalex.org/I3133134087"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":1.9182,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.85586537,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"7","issue":null,"first_page":"102313","last_page":"102320"},"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":0.9940999746322632,"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/T11298","display_name":"Synthesis and Properties of Aromatic Compounds","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7048103213310242},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5398613214492798},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.40781906247138977},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3661288321018219},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3283916711807251},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28843557834625244}],"concepts":[{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7048103213310242},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5398613214492798},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.40781906247138977},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3661288321018219},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3283916711807251},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28843557834625244}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2019.2931406","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2931406","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08777072.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c798ec08a3964b4193e00927e145c320","is_oa":true,"landing_page_url":"https://doaj.org/article/c798ec08a3964b4193e00927e145c320","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 7, Pp 102313-102320 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2931406","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2931406","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08777072.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2082826544","display_name":null,"funder_award_id":"Postdoctoral","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2199675829","display_name":null,"funder_award_id":"1701081B","funder_id":"https://openalex.org/F4320335473","funder_display_name":"Postdoctoral Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G3065972664","display_name":null,"funder_award_id":"11601006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3218190166","display_name":null,"funder_award_id":"2017M621579","funder_id":"https://openalex.org/F4320335473","funder_display_name":"Postdoctoral Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5027569125","display_name":null,"funder_award_id":"11561042","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5612697103","display_name":null,"funder_award_id":"2017M","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5797785011","display_name":null,"funder_award_id":"16010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7765875064","display_name":null,"funder_award_id":"1701081B","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G8208342437","display_name":null,"funder_award_id":"1 and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G828030330","display_name":null,"funder_award_id":"2017M621579","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320335473","display_name":"Postdoctoral Science Foundation of Jiangsu Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2966452567.pdf","grobid_xml":"https://content.openalex.org/works/W2966452567.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W307860179","https://openalex.org/W1022727114","https://openalex.org/W1542938076","https://openalex.org/W1995058487","https://openalex.org/W2006975882","https://openalex.org/W2010313563","https://openalex.org/W2010760701","https://openalex.org/W2023258618","https://openalex.org/W2030654245","https://openalex.org/W2031733386","https://openalex.org/W2064470072","https://openalex.org/W2067696638","https://openalex.org/W2079345050","https://openalex.org/W2083951382","https://openalex.org/W2205851424","https://openalex.org/W2346953669","https://openalex.org/W2467335949","https://openalex.org/W2584743269","https://openalex.org/W2746084420","https://openalex.org/W2789572801","https://openalex.org/W2794124357","https://openalex.org/W2804035460","https://openalex.org/W2964034284","https://openalex.org/W4243449554","https://openalex.org/W4247782380"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W3111310291"],"abstract_inverted_index":{"Let":[0],"Q(G)":[1,86,100],"be":[2],"the":[3,64,116],"graph":[4,65,144],"derived":[5,66],"from":[6,67],"G":[7,17,38,43,49,58,69,74,91,105,126,136,145,151,156],"by":[8,19,48,79],"inserting":[9],"a":[10],"new":[11,24],"vertex":[12,89,103],"into":[13],"every":[14,81,88,96,102],"edge":[15],"of":[16,22,31,36,85,90,99,104,122,141,150],"and":[18,33,42,73,95,119,146,155],"connecting":[20,80],"edges":[21,30],"these":[23],"vertices":[25],"that":[26],"are":[27],"on":[28],"adjacent":[29],"G,":[32,37],"Q-double":[34,123],"join":[35,124],"<sub":[39,44,54,59,70,75,92,106,132,137,152,157],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[40,45,51,55,60,71,76,93,107,128,133,138,153,158],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[41,56,72,94,134,154],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[46,61,77,108,139,159],"denoted":[47],"<sup":[50,127],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Q</sup>":[52,129],"v{G":[53],",":[57,78,135],"},":[62],"is":[63],"Q(G),":[68],"old-vertex":[82],"V":[83],"(G)":[84],"with":[87,101],"new-vertex":[97],"I(G)":[98],".":[109,160],"In":[110],"this":[111],"paper,":[112],"we":[113],"mainly":[114],"considered":[115],"resistance":[117],"distance":[118],"Kirchhoff":[120],"index":[121],"graphs":[125,149],"v":[130],"{G":[131],"}":[140],"an":[142],"r-regular":[143],"any":[147],"two":[148]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
