{"id":"https://openalex.org/W2559241849","doi":"https://doi.org/10.1051/ita/2016027","title":"The average scattering number of graphs","display_name":"The average scattering number of graphs","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2559241849","doi":"https://doi.org/10.1051/ita/2016027","mag":"2559241849"},"language":"en","primary_location":{"id":"doi:10.1051/ita/2016027","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita/2016027","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"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"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.numdam.org/item/10.1051/ita/2016027.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056662953","display_name":"Ersin Aslan","orcid":"https://orcid.org/0000-0002-5496-2075"},"institutions":[{"id":"https://openalex.org/I16748637","display_name":"Manisa Celal Bayar University","ror":"https://ror.org/053f2w588","country_code":"TR","type":"education","lineage":["https://openalex.org/I16748637"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Ersin Aslan","raw_affiliation_strings":["Turgutlu Vocational Training School, Celal Bayar University, 45400 Manisa, Turkey"],"affiliations":[{"raw_affiliation_string":"Turgutlu Vocational Training School, Celal Bayar University, 45400 Manisa, Turkey","institution_ids":["https://openalex.org/I16748637"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028567435","display_name":"Deniz K\u0131l\u0131n\u00e7","orcid":"https://orcid.org/0000-0002-2336-8831"},"institutions":[{"id":"https://openalex.org/I16748637","display_name":"Manisa Celal Bayar University","ror":"https://ror.org/053f2w588","country_code":"TR","type":"education","lineage":["https://openalex.org/I16748637"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Deniz Kilin\u00e7","raw_affiliation_strings":["Department of Software Engineering, Celal Bayar University, 45400 Manisa, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Software Engineering, Celal Bayar University, 45400 Manisa, Turkey","institution_ids":["https://openalex.org/I16748637"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002657270","display_name":"Fatih Y\u00fccalar","orcid":"https://orcid.org/0000-0002-1006-2227"},"institutions":[{"id":"https://openalex.org/I16748637","display_name":"Manisa Celal Bayar University","ror":"https://ror.org/053f2w588","country_code":"TR","type":"education","lineage":["https://openalex.org/I16748637"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Fatih Y\u00fccalar","raw_affiliation_strings":["Fatih Y\u00fccalar, Department of Software Engineering, Celal Bayar University, 45400 Manisa, Turkey"],"affiliations":[{"raw_affiliation_string":"Fatih Y\u00fccalar, Department of Software Engineering, Celal Bayar University, 45400 Manisa, Turkey","institution_ids":["https://openalex.org/I16748637"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019378858","display_name":"Emin Boranda\u011f","orcid":"https://orcid.org/0000-0001-5553-2707"},"institutions":[{"id":"https://openalex.org/I16748637","display_name":"Manisa Celal Bayar University","ror":"https://ror.org/053f2w588","country_code":"TR","type":"education","lineage":["https://openalex.org/I16748637"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Emin Boranda\u011f","raw_affiliation_strings":["Emin Boranda\u011f, Department of Software Engineering, Celal Bayar University, 45400 Manisa, Turkey"],"affiliations":[{"raw_affiliation_string":"Emin Boranda\u011f, Department of Software Engineering, Celal Bayar University, 45400 Manisa, Turkey","institution_ids":["https://openalex.org/I16748637"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5056662953"],"corresponding_institution_ids":["https://openalex.org/I16748637"],"apc_list":null,"apc_paid":null,"fwci":1.1486,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79449097,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"3","first_page":"263","last_page":"272"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9919999837875366,"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":0.9811999797821045,"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":0.6554837226867676},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6528118252754211},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.5879717469215393},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5436110496520996},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4610205888748169},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4455050528049469},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.4172735810279846},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.41392314434051514},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1934613287448883},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.17433393001556396},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06012633442878723}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6554837226867676},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6528118252754211},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.5879717469215393},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5436110496520996},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4610205888748169},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4455050528049469},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.4172735810279846},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.41392314434051514},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1934613287448883},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.17433393001556396},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06012633442878723}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ita/2016027","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita/2016027","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"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"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:ITA_2016__50_3_263_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ita/2016027/","pdf_url":"https://www.numdam.org/item/10.1051/ita/2016027.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:numdam.org:ITA_2016__50_3_263_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ita/2016027/","pdf_url":"https://www.numdam.org/item/10.1051/ita/2016027.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2559241849.pdf","grobid_xml":"https://content.openalex.org/works/W2559241849.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1975099798","https://openalex.org/W1986359845","https://openalex.org/W2012572972","https://openalex.org/W2047797996","https://openalex.org/W2055745794","https://openalex.org/W2093816675","https://openalex.org/W2167562659","https://openalex.org/W2799004609"],"related_works":["https://openalex.org/W4313216298","https://openalex.org/W2071797893","https://openalex.org/W2097063382","https://openalex.org/W2384431448","https://openalex.org/W3002741190","https://openalex.org/W2188756358","https://openalex.org/W3189256254","https://openalex.org/W3217780850","https://openalex.org/W2884117239","https://openalex.org/W2055455751"],"abstract_inverted_index":{"The":[0,71,134],"scattering":[1,73,104,127,136,150],"number":[2,74,96,105,128,137,151],"of":[3,9,12,26,30,66,75,97,111,114,138,152],"a":[4,7,13,20,27,36,39,109,115],"graph":[5,41,100,140,156],"is":[6,35,59,80,108,119],"measure":[8,110],"the":[10,24,31,57,95,103,112,123,148],"vulnerability":[11,113],"graph.":[14],"In":[15],"this":[16,107],"paper":[17],"we":[18],"investigate":[19],"refinement":[21],"that":[22,68],"involves":[23],"average":[25,72,126,135,149],"local":[28],"version":[29],"parameter.":[32],"If":[33],"v":[34],"vertex":[37],"in":[38,99],"connected":[40],"G,":[42],"then":[43],"scv(G)":[44,88],"=":[45,84],"max":[46],"{":[47],"\u03c9(G":[48],"\u2212":[49,51],"Sv)":[50],"|":[52,54],"Sv":[53,65],"},":[55],"where":[56,91],"maximum":[58],"taken":[60],"over":[61],"all":[62],"disconnecting":[63],"sets":[64],"G":[67,76],"contain":[69],"v.":[70],"denoted":[77],"by":[78,155],"scav(G),":[79],"defined":[81],"as":[82],"scav(G)":[83],"\u03a3v":[85],"\u2208":[86],"V(G)":[87],"/":[89],"n,":[90],"n":[92],"will":[93],"denote":[94],"vertices":[98],"G.":[101],"Like":[102],"itself,":[106],"graph,":[116],"but":[117],"it":[118],"more":[120],"sensitive.":[121],"Next,":[122],"relations":[124],"between":[125],"and":[129],"other":[130],"parameters":[131],"are":[132,142,158],"determined.":[133],"some":[139,145],"classes":[141],"obtained.":[143],"Moreover,":[144],"results":[146],"about":[147],"graphs":[153],"obtained":[154],"operations":[157],"given.":[159]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}