{"id":"https://openalex.org/W4402299357","doi":"https://doi.org/10.1051/ro/2024175","title":"Expected value for the k-distance degree index of a graph","display_name":"Expected value for the k-distance degree index of a graph","publication_year":2024,"publication_date":"2024-09-06","ids":{"openalex":"https://openalex.org/W4402299357","doi":"https://doi.org/10.1051/ro/2024175"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2024175","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024175","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/06/ro240002.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/06/ro240002.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043112264","display_name":"hamideh Aram","orcid":null},"institutions":[{"id":"https://openalex.org/I4210124016","display_name":"Islamic Azad University, Khoy Branch","ror":"https://ror.org/038bemd25","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210124016"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Hamideh Aram","raw_affiliation_strings":["Department of Mathematics, Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran"],"raw_orcid":"https://orcid.org/0000-0003-3894-9214","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran","institution_ids":["https://openalex.org/I4210124016"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043112264"],"corresponding_institution_ids":["https://openalex.org/I4210124016"],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":null,"fwci":0.7998,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.70099899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":94},"biblio":{"volume":"58","issue":"6","first_page":"5159","last_page":"5166"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"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":1.0,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9965999722480774,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9951000213623047,"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/index","display_name":"Index (typography)","score":0.5696064829826355},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.533598005771637},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5269872546195984},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.476574182510376},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.47231313586235046},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.471321165561676},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40577614307403564},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23015612363815308},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17850440740585327},{"id":"https://openalex.org/keywords/world-wide-web","display_name":"World Wide Web","score":0.08611103892326355}],"concepts":[{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.5696064829826355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.533598005771637},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5269872546195984},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.476574182510376},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.47231313586235046},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.471321165561676},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40577614307403564},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23015612363815308},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17850440740585327},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.08611103892326355},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1051/ro/2024175","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024175","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/06/ro240002.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1051/ro/2024175","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024175","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/06/ro240002.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4402299357.pdf","grobid_xml":"https://content.openalex.org/works/W4402299357.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W2016496752","https://openalex.org/W2069962626","https://openalex.org/W2076274021","https://openalex.org/W2115325963","https://openalex.org/W2154117231","https://openalex.org/W2318794083","https://openalex.org/W2989290433","https://openalex.org/W3045222397","https://openalex.org/W4304806295"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2399035783","https://openalex.org/W3161230432","https://openalex.org/W4367190712","https://openalex.org/W2168900540","https://openalex.org/W1487201914","https://openalex.org/W4301429470","https://openalex.org/W280458463","https://openalex.org/W1170131723","https://openalex.org/W2125310826"],"abstract_inverted_index":{"For":[0],"a":[1,34],"graph":[2],"G,":[3],"the":[4,22,26,45,52],"k-distance":[5,30],"degree":[6,31],"index":[7,32,50],"is":[8],"N\u03ba(G)":[9],"=":[10],"\u2211\u03ba=1diam(G)":[11],"(":[12],"\u2211w\u2208V(G)":[13],"d\u03ba(w)":[14],")":[15],"\u03ba.":[16],"In":[17],"this":[18,49],"article,":[19],"we":[20,43],"calculate":[21],"accurate":[23],"formula":[24],"of":[25,48,54],"expected":[27],"value":[28,47],"for":[29],"in":[33,51],"random":[35],"arranged":[36,57],"polygonal":[37,58],"string":[38],"with":[39],"m-arranged":[40],"polygons.":[41],"Finally,":[42],"determine":[44],"average":[46],"collection":[53],"all":[55],"those":[56],"strings.":[59]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2024-09-07T00:00:00"}
