{"id":"https://openalex.org/W2898860148","doi":"https://doi.org/10.1109/access.2018.2876460","title":"Discharging Approach for Double Roman Domination in Graphs","display_name":"Discharging Approach for Double Roman Domination in Graphs","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2898860148","doi":"https://doi.org/10.1109/access.2018.2876460","mag":"2898860148"},"language":"en","primary_location":{"id":"doi:10.1109/access.2018.2876460","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2018.2876460","pdf_url":null,"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":null,"license_id":null,"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://doi.org/10.1109/access.2018.2876460","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012636371","display_name":"Zehui Shao","orcid":"https://orcid.org/0000-0003-0764-4135"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zehui Shao","raw_affiliation_strings":["Institute of Computing Science and Technology, Guangzhou University, Guangzhou, China","ORCiD"],"raw_orcid":"https://orcid.org/0000-0003-0764-4135","affiliations":[{"raw_affiliation_string":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou, China","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"ORCiD","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014510022","display_name":"Pu Wu","orcid":"https://orcid.org/0000-0002-1179-5748"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pu Wu","raw_affiliation_strings":["Institute of Computing Science and Technology, Guangzhou University, Guangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032769891","display_name":"Huiqin Jiang","orcid":"https://orcid.org/0000-0002-3316-877X"},"institutions":[{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huiqin Jiang","raw_affiliation_strings":["School of Information Science and Engineering, Chengdu University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Chengdu University, Chengdu, China","institution_ids":["https://openalex.org/I4210125143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100711426","display_name":"Zepeng Li","orcid":"https://orcid.org/0000-0003-0843-8536"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zepeng Li","raw_affiliation_strings":["School of Information Science and Engineering, Lanzhou University, Lanzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Lanzhou University, Lanzhou, China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089379545","display_name":"Janez \u017derovnik","orcid":"https://orcid.org/0000-0002-6041-1106"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]},{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Janez Zerovnik","raw_affiliation_strings":["Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia","Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I4210106342"]},{"raw_affiliation_string":"Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109452577","display_name":"Xiujun Zhang","orcid":"https://orcid.org/0000-0002-6704-031X"},"institutions":[{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiujun Zhang","raw_affiliation_strings":["School of Information Science and Engineering, Chengdu University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Chengdu University, Chengdu, China","institution_ids":["https://openalex.org/I4210125143"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":1.8977,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.87813654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"6","issue":null,"first_page":"63345","last_page":"63351"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994000196456909,"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/T12288","display_name":"Optimization and Search Problems","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/computer-science","display_name":"Computer science","score":0.5724447965621948}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5724447965621948}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1109/access.2018.2876460","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2018.2876460","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/299727","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/299727","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/403544","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/403544","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal article (JA)"},{"id":"pmh:oai:doaj.org/article:7622913bb80b4af6b5a69ece6c76b4ff","is_oa":true,"landing_page_url":"https://doaj.org/article/7622913bb80b4af6b5a69ece6c76b4ff","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,"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":"IEEE Access, Vol 6, Pp 63345-63351 (2018)","raw_type":"article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/268399","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/268399","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"\u671f\u520a\u8bba\u6587"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/280357","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/280357","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/292021","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/292021","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1109/access.2018.2876460","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2018.2876460","pdf_url":null,"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":null,"license_id":null,"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/G1597118509","display_name":null,"funder_award_id":"lzujbky-2018-37","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G4236846175","display_name":null,"funder_award_id":"61802158","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4802069527","display_name":null,"funder_award_id":"2017JY0095","funder_id":"https://openalex.org/F4320333337","funder_display_name":"Applied Basic Research Program of Sichuan Province"},{"id":"https://openalex.org/G8056387268","display_name":null,"funder_award_id":"2017YFB0802300","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G824826531","display_name":null,"funder_award_id":"61672050","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320333337","display_name":"Applied Basic Research Program of Sichuan Province","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1493071618","https://openalex.org/W1493972574","https://openalex.org/W1968103577","https://openalex.org/W1983482338","https://openalex.org/W1984228559","https://openalex.org/W1992039414","https://openalex.org/W2021542025","https://openalex.org/W2025437641","https://openalex.org/W2045251507","https://openalex.org/W2052351239","https://openalex.org/W2058200262","https://openalex.org/W2058946695","https://openalex.org/W2076590268","https://openalex.org/W2090249824","https://openalex.org/W2147353440","https://openalex.org/W2147601521","https://openalex.org/W2346913169","https://openalex.org/W2465902253","https://openalex.org/W2466044249","https://openalex.org/W2519091437","https://openalex.org/W2752270036"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"The":[0,52,123],"discharging":[1,43,54],"method":[2],"is":[3,59,130,145],"most":[4],"well-known":[5],"for":[6,56,86],"its":[7],"central":[8],"role":[9],"in":[10,30],"the":[11,14,66,99,103,109,116],"proof":[12,19],"of":[13,102,108],"Four":[15],"Color":[16],"Theorem.":[17],"This":[18],"technique":[20,44],"was":[21],"extensively":[22],"applied":[23],"to":[24],"study":[25],"various":[26],"graph":[27,89],"coloring":[28],"problems,":[29],"particular":[31],"on":[32,49,61,70],"planar":[33],"graphs.":[34,74],"In":[35],"this":[36,77],"paper,":[37],"we":[38,79,96],"show":[39],"that":[40,82,127],"suitably":[41],"altered":[42],"can":[45],"also":[46,97],"be":[47],"used":[48],"domination-type":[50,57,64],"problems.":[51],"general":[53],"approach":[55],"problems":[58],"illustrated":[60],"a":[62],"specific":[63],"problem,":[65],"double":[67,104,117,131,146],"Roman":[68,105,132,147],"domination":[69,106],"some":[71],"generalized":[72,110,118],"Petersen":[73,111,119],"By":[75],"applying":[76],"approach,":[78],"first":[80],"prove":[81],"\u03b3dR(G)\u2265(3n/\u0394(G)":[83],"+":[84],"1)":[85,114,129,144],"any":[87],"connected":[88],"G":[90],"with":[91],"n\u22652":[92],"vertices.":[93],"As":[94],"examples,":[95],"determine":[98],"exact":[100],"values":[101],"numbers":[107],"graphs":[112,120],"P(n,":[113,128],"and":[115,134,142,149],"DP(n,":[121,143],"1).":[122],"obtained":[124],"results":[125],"imply":[126],"if":[133,136,148,151],"only":[135,150],"n":[137,152],"\u2260":[138],"2":[139],"(mod":[140,155],"4)":[141],"\u2261":[153],"0":[154],"4).":[156]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}