{"id":"https://openalex.org/W3084098709","doi":"https://doi.org/10.1016/j.heliyon.2020.e04786","title":"Complexity trees of the sequence of some nonahedral graphs generated by triangle","display_name":"Complexity trees of the sequence of some nonahedral graphs generated by triangle","publication_year":2020,"publication_date":"2020-09-01","ids":{"openalex":"https://openalex.org/W3084098709","doi":"https://doi.org/10.1016/j.heliyon.2020.e04786","mag":"3084098709","pmid":"https://pubmed.ncbi.nlm.nih.gov/32964151","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/7490826"},"language":"en","primary_location":{"id":"doi:10.1016/j.heliyon.2020.e04786","doi":"https://doi.org/10.1016/j.heliyon.2020.e04786","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.heliyon.2020.e04786","pdf_url":"http://www.cell.com/article/S2405844020316297/pdf","source":{"id":"https://openalex.org/S2898612692","display_name":"Heliyon","issn_l":"2405-8440","issn":["2405-8440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","ki-jl-1","norway-1","poland-40","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Heliyon","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://www.cell.com/article/S2405844020316297/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007160556","display_name":"Salama Nagy Daoud","orcid":"https://orcid.org/0000-0003-3809-2521","observed_orcids":["https://orcid.org/0000-0003-3809-2521"]},"institutions":[{"id":"https://openalex.org/I23075662","display_name":"Taibah University","ror":"https://ror.org/01xv1nn60","country_code":"SA","type":"education","lineage":["https://openalex.org/I23075662"]},{"id":"https://openalex.org/I63601056","display_name":"Menoufia University","ror":"https://ror.org/05sjrb944","country_code":"EG","type":"education","lineage":["https://openalex.org/I63601056"]}],"countries":["EG","SA"],"is_corresponding":true,"raw_author_name":"S.N. Daoud","raw_affiliation_strings":["Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El Kom 32511, Egypt","Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El Kom 32511, Egypt","institution_ids":["https://openalex.org/I63601056"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia","institution_ids":["https://openalex.org/I23075662"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014836528","display_name":"Wedad Saleh","orcid":"https://orcid.org/0000-0003-0600-2624","observed_orcids":["https://orcid.org/0000-0003-0600-2624","https://orcid.org/0000-0002-7389-3183"]},"institutions":[{"id":"https://openalex.org/I23075662","display_name":"Taibah University","ror":"https://ror.org/01xv1nn60","country_code":"SA","type":"education","lineage":["https://openalex.org/I23075662"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Wedad Saleh","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia","institution_ids":["https://openalex.org/I23075662"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007160556"],"corresponding_institution_ids":["https://openalex.org/I23075662","https://openalex.org/I63601056"],"apc_list":{"value":1750,"currency":"USD","value_usd":1750},"apc_paid":{"value":1750,"currency":"USD","value_usd":1750},"fwci":0.3037,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.47623892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"6","issue":"9","first_page":"e04786","last_page":"e04786"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9951000213623047,"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/T11476","display_name":"Graph theory and applications","score":0.9951000213623047,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.0017000000225380063,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.00139999995008111,"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/spanning-trees","display_name":"spanning trees","score":0.8930000066757202},{"id":"https://openalex.org/keywords/polyhedral-graphs","display_name":"polyhedral graphs","score":0.8130000233650208},{"id":"https://openalex.org/keywords/recurrence-relations","display_name":"recurrence relations","score":0.871999979019165},{"id":"https://openalex.org/keywords/explicit-formula","display_name":"explicit formula","score":0.7409999966621399},{"id":"https://openalex.org/keywords/graph-entropy","display_name":"graph entropy","score":0.890999972820282},{"id":"https://openalex.org/keywords/average-degree","display_name":"average degree","score":0.7099999785423279}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7203442454338074},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6745332479476929},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.5471105575561523},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5101178288459778},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45189690589904785},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.429909884929657},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4054211378097534},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1984393298625946},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/j.heliyon.2020.e04786","doi":"https://doi.org/10.1016/j.heliyon.2020.e04786","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.heliyon.2020.e04786","pdf_url":"http://www.cell.com/article/S2405844020316297/pdf","source":{"id":"https://openalex.org/S2898612692","display_name":"Heliyon","issn_l":"2405-8440","issn":["2405-8440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","ki-jl-1","norway-1","poland-40","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Heliyon","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:7490826","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7490826","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Heliyon","raw_type":"Text"},{"id":"pmid:32964151","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/32964151","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Heliyon","raw_type":"Journal Article"},{"id":"pmh:oai:doaj.org/article:30ecc48cb3024c0d927d93c8efab569c","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/30ecc48cb3024c0d927d93c8efab569c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Heliyon, Vol 6, Iss 9, Pp e04786- (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1016/j.heliyon.2020.e04786","doi":"https://doi.org/10.1016/j.heliyon.2020.e04786","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.heliyon.2020.e04786","pdf_url":"http://www.cell.com/article/S2405844020316297/pdf","source":{"id":"https://openalex.org/S2898612692","display_name":"Heliyon","issn_l":"2405-8440","issn":["2405-8440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","ki-jl-1","norway-1","poland-40","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Heliyon","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321161","display_name":"Taibah University","ror":"https://ror.org/01xv1nn60"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3084098709.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W346379343","https://openalex.org/W626292722","https://openalex.org/W1515707356","https://openalex.org/W1589331344","https://openalex.org/W1888793072","https://openalex.org/W1965922183","https://openalex.org/W1977182421","https://openalex.org/W1978886755","https://openalex.org/W1985099574","https://openalex.org/W1987430956","https://openalex.org/W1988445930","https://openalex.org/W1997371824","https://openalex.org/W2013872122","https://openalex.org/W2029673229","https://openalex.org/W2032081889","https://openalex.org/W2061309095","https://openalex.org/W2068861748","https://openalex.org/W2069680987","https://openalex.org/W2179119116","https://openalex.org/W2483722916","https://openalex.org/W2539956009","https://openalex.org/W2742401916","https://openalex.org/W2902620750","https://openalex.org/W2919107023","https://openalex.org/W2945335975","https://openalex.org/W4238426377"],"related_works":["https://openalex.org/W7217677380","https://openalex.org/W2922366535","https://openalex.org/W4407790245","https://openalex.org/W4409753529","https://openalex.org/W4406053574","https://openalex.org/W2952175180","https://openalex.org/W4406818212","https://openalex.org/W4408165523","https://openalex.org/W4414390572","https://openalex.org/W2792700515"],"abstract_inverted_index":{"Calculating":[0],"the":[1,12,18,33,37,43,62,69],"number":[2,38],"of":[3,6,11,28,39,45,61,71],"spanning":[4,40],"trees":[5,41],"a":[7],"graph":[8,15],"is":[9],"one":[10],"widely":[13],"studied":[14,78],"problems":[16],"since":[17],"Pioneer":[19],"Gustav":[20],"Kirchhoff":[21],"(1847).":[22],"In":[23],"this":[24,74],"work,":[25],"using":[26,55],"knowledge":[27],"difference":[29],"equations":[30],"we":[31,67],"drive":[32],"explicit":[34],"formulas":[35],"for":[36],"in":[42,73],"sequence":[44],"some":[46],"Nonahedral":[47],"(nine":[48],"faced":[49],"polyhedral)":[50],"graphs":[51,72,79],"generated":[52],"by":[53],"triangle":[54],"electrically":[56],"equivalent":[57],"transformations":[58],"and":[59,87],"rules":[60],"weighted":[63],"generating":[64],"function.":[65],"Finally,":[66],"evaluate":[68],"entropy":[70],"manuscript":[75],"with":[76,80],"different":[77],"an":[81],"average":[82],"degree":[83],"being":[84],"4,":[85],"5":[86],"6.":[88]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2020-09-14T00:00:00"}
