{“id”：“https://openalex.org/W2143198086“，”doi“：”https://doi.org/10.1155/2015/320616“，”title“：”On（a，1）-正则图的顶点反魔术边标记“，”display_name“：”On（a，l）-正则图形的顶点反魔法边标记“（publication_year）：2015，”publication_date“：”2015-01-01“，”ids“：{”openalex“：”https://openalex.org/W2143198086“，”doi“：”https://doi.org/10.1155/2015/320616“，”mag“：”2143198086“}，”language“：”en“，”primary_location“：{”is_oa“：true，”landing_page_url“：”https://doi.org/10.1155/2015/320616，“pdf_url”：http://downloads.hindawi.com/journals/jam/2015/320616.pdf，“源”：{“id”：https://openalex.org/S190082376“，”display_name“：”Journal of applicated mathematics“，”issn_l“：”1110-757X“，”isn“：[”1110-75%“，”1687-0042“]，”is_oa“：true，”is_in_doaj“：true，”host_organization“：”https://openalex.org/P4310319869“，”“host_organization_name”：“Hindawi Publishing Corporation”，“host_organization_lineage”：[“https://openalex.org/P4310319869“]，”host_organization_lineage_names“：[”Hindawi Publishing Corporation“]，“type”：“journal”}，“license”：“cc-by”，“licence_id”：“https://openalex.org/licenses/cc-by“，”version“：”publishedVersion“，”is_accepted“：true，”is_published“：true}，”type“：”article“，”type_crossref“：“journal-article”，”indexed_in“：[”crossref“，”doaj“]，”open_access“：{”is_oa“：true，”oa_status“：”gold“，”oa_url“：”http://downloads.hindawi.com/journals/jam/2015/320616.pdf“，”any_repository_has_fulltext“：true}，”authorships“：[{”author_position“：”第一“，”作者“：{”id“：”https://openalex.org/A5046747547“，”display_name“：”Martin Ba\u010da“，”orcid“：”https://orcid.org/0000-0002-5758-0347}，“机构”：[{“id”：https://openalex.org/I183764125“，”display_name“：”韩国科技大学\u0161ice“，”ror“：”https://ror.org/05xm08015“，”country_code“：”SK“，”type“：“教育”，”世系“：[”https://openalex.org/I183764125“]}]，”国家“：[”SK“]，”is_corresponding“：false，”raw_author_name“：”Martin Ba\u010da“，”raw _ afiliation_strings“：[“斯洛伐克理工大学应用数学与信息学系，Letn\u00e1 9，04200 Ko\u0161ice”]，”从属关系“：[{”raw_ afiliation _string“：”斯洛伐克科技大学应用数学和信息学系，Letn\u00e1 9，04200 Ko\u0161ice“，“institution_ids”：[“https://openalex.org/I183764125“]}]}，{”author_position“：”middle“，”author“：{”id“：”https://openalex.org/A5033804594“，”display_name“：”Andrea Semani\u010dov\u00e1\u2013Fe\u0148ov\u010d\u00edkov\u100e1“，”orcid“：”https://orcid.org/0000-0002-8432-9836}，“机构”：[{“id”：https://openalex.org/I183764125“，”display_name“：”Ko\u0161ice科技大学“，”ror“：”https://ror.org/05xm08015“，”country_code“：”SK“，”type“：“教育”，”世系“：[”https://openalex.org/I183764125“]}]，”countries“：[”SK“]，”is_corresponding“：false，”raw_author_name“：”Andrea Semani\u010dov\u00e1-Fe\u0148ov\u010d\u00edkov\u000e1“，”raw _ affiliation_strings“：【”斯洛伐克理工大学应用数学与信息学系，Letn\u00e 9，04200 Ko\u0161ice“】，”affiliation“：[{”raw _affiliation_string“：”斯洛伐克科技大学应用数学和信息学系，Letn\u00e1 9，04200 Ko\u0161ice“，“institution_ids”：[“https://openalex.org/I183764125“]}]}，{”author_position“：”middle“，”author“：{”id“：”https://openalex.org/A5036266606“，”display_name“：”淘名王“，”兽人“：”https://orcid.org/0000-0002-3432-8579}，“机构”：[{“id”：https://openalex.org/I169090423“，”display_name“：”东海大学“，”ror“：”https://ror.org/00zhvdn11“，”country_code“：”TW“，”type“：“教育”，”世系“：[”https://openalex.org/I169090423“]}]，”countries“：[”TW“]，”is_corresponding“：true，”raw_author_name“：”Tao-Ming Wang“，”rau_affiliation_strings“：【”台湾台中市东海大学应用数学系40704“】，”affiliations“：[{”raw_affiliation_string“：”台湾台中和市东海学院应用数学系，“institution_ids”：【”https://openalex.org/I169090423“]}]}，{”author_position“：”last“，”author“：{”id“：”https://openalex.org/A5089640773“，”display_name“：”Guanghui Zhang“，”orcid“：”https://orcid.org/0009-0002-6622-0308}，“机构”：[{“id”：https://openalex.org/I162838928“，”display_name“：”国立中兴大学“，”ror“：”https://ror.org/05vn3ca78“，”country_code“：”TW“，”type“：“教育”，”世系“：[”https://openalex.org/I162838928“]}]，”国家“：[”TW“]，”is_corresponding“：false，”raw_author_name“：”Guang-Hui Zhang“，”raw _affiliation_strings“：[“台湾台中402国立中兴大学应用数学系”]，”affiliations“：[{”raw _affiliation_string“：”台湾台中四百零二国立中兴学院应用数学系“，”机构ID“：[”https://openalex.org/I162838928“]}]}]，”countries_disticont_count“：2，”institutions_disticent_count”：3，”corresponding_author_ids“：[”https://openalex.org/A5036266606“]，”对应的机构ID“：[”https://openalex.org/I169090423“]，”apc_list“：{“value”：1025，”currency“：”USD“，”value_USD“：1025、”provenance“：”doaj“}、”apc_payed“：”{“value”：1024、”currentary“：”美元“，”value_USD”：1025.“provenance”：“doaj”}、“has_fulltext”：true、“fulltext_origin”：“pdf”、“cited_by_count”：3、“citecd_by_percentile_year”：{”min“：80，“max”：82}，“biblio”：{“volume”：“2015”，“issue”：null，“first_page”：“1”，“last_page”：”7“}，“is_retracted“：false，”is_paratext“：fase，”primary_topic“：{”id“：”https://openalex.org/T12541“，”display_name“：”图形标记和维度问题“，”score“：0.9999，”subfield“：{”id“：”https://openalex.org/subfields/1703“，”display_name“：”计算理论与数学“}，”字段“：{”id“：”https://openalex.org/fields/17“，”display_name“：”Computer Science“}，”domain“：{”id“：”https://openalex.org/domains/3“，”display_name“：”物理科学“}}，”主题“：[{”id“：”https://openalex.org/T12541“，”display_name“：”图形标记和维度问题“，”score“：0.9999，”subfield“：{”id“：”https://openalex.org/subfields/1703“，”display_name“：”计算理论与数学“}，”字段“：{”id“：”https://openalex.org/fields/17“，”display_name“：”Computer Science“}，”domain“：{”id“：”https://openalex.org/domains/3“，”display_name“：”物理科学“}}]，”关键词“：[{”id“：”https://openalex.org/keywords/antimagic-labeling“，”display_name“：”反魔法标签“，”score“：0.57971}，{”id“：”https://openalex.org/keywords/graph-labeling“，”display_name“：”Graph Labeling“，”score“：0.562602}，{”id“：”https://openalex.org/keywords/total-edge-irregularity网站“，”“display_name”：“总边缘不规则度”，“score”：0.517392}，{“id”：“https://openalex.org/keywords/edge-coloring网站“，”display_name“：”Edge Coloring“，”score“：0.500926}]，”concepts“：[{”id“：”https://openalex.org/C11413529，“wikidata”：https://www.wikidata.org/wiki/Q8366“，”display_name“：”Algorithm“，”level“：1，”score“：0.5435772}，{”id“：”https://openalex.org/C154945302，“wikidata”：https://www.wikidata.org/wiki/Q11660“，”display_name“：”人工智能“，”level“：1，”score“：0.36166263}，{”id“：”https://openalex.org/C41008148，“wikidata”：https://www.wikidata.org/wiki/Q21198（网址：https://www.wikidata.org/wiki/Q21198）“，”display_name“：”计算机科学“，”level“：0，”score“：0.28900748}]，”mesh“：[]，”locations_count“：3，”location“：[{”is_oa“：true，”landing_page_url“：”https://doi.org/10.1155/2015/320616，“pdf_url”：http://downloads.hindawi.com/journals/jam/2015/320616.pdf，“源”：{“id”：https://openalex.org/S190082376“，”display_name“：”Journal of applicated mathematics“，”issn_l“：”1110-757X“，”isn“：[”1110-75%“，”1687-0042“]，”is_oa“：true，”is_in_doaj“：true，”host_organization“：”https://openalex.org/P4310319869“，”“host_organization_name”：“Hindawi Publishing Corporation”，“host_organization_lineage”：[“https://openalex.org/P4310319869“]，”host_organization_lineage_names“：[”Hindawi Publishing Corporation“]，“type”：“journal”}，“license”：“cc-by”，“licence_id”：“https://openalex.org/licenses/cc-by“，”version“：”publishedVersion“，”is_accepted“：true，”is_published“：true}，{”is_oa“：false，”landing_page_url“：”https://doaj.org/article/e93d41ad687340738161a3471d29f659“，”pdf_url“：空，”源“：{”id“：”https://openalex.org/S4306401280“，”display_name“：”DOAJ（DOAJ：开放存取期刊目录）“，”issn_l“：null，”issn“：null:”is_oa“：true，”is_in_DOAJ“：false，”host_organization“：null，”host_organization_name“:null，“host_orgganization_lineage”：[]，“host_orgganization _lineage_names”：[[]，“type”：“repository”}，“license”：null、“license_id”：null、“version”：null.、“is_accepted”：false、“is_published“：false｝，｛”is_oa“：true，”landing_page_url“：”http://projecteuclid.org/euclid.jam/1439816406，“pdf_url”：https://project欧几里得.org/journals/journal-of-applied-mathematics/volume-2015/issue-none/On---a--1---Vertex-Antimagic-Edge/10.1155/2015/320616.pdf，“源”：{“id”：https://openalex.org/S4306400787“，”display_name“：”欧几里德项目（康奈尔大学）“，”issn_l“：null，”issn“：null，”is_oa“：true，”is_ in_doaj“：false，”host_organization“：”https://openalex.org/I205783295“，”“host_organization_name”：“康奈尔大学”，“host_organization_lineage”：[“https://openalex.org/I205783295“]，”host_organization_lineage_names“：[”康奈尔大学“]，“type”：“repository”}，“license”：“cc-by”，“licence_id”：“https://openalex.org/licenses/cc-by“，”version“：”publishedVersion“，”is_accepted“：true，”is_published“：true}]，”best_oa_location“：{”is_oa“：true，”landing_page_url“：”https://doi.org/10.1155/2015/320616，“pdf_url”：http://downloads.hindawi.com/journals/jam/2015/320616.pdf，“源”：{“id”：https://openalex.org/S190082376“，”display_name“：”Journal of applicated mathematics“，”issn_l“：”1110-757X“，”isn“：[”1110-75%“，”1687-0042“]，”is_oa“：true，”is_in_doaj“：true，”host_organization“：”https://openalex.org/P4310319869“，”“host_organization_name”：“Hindawi Publishing Corporation”，“host_organization_lineage”：[“https://openalex.org/P4310319869“]，”host_organization_lineage_names“：[”Hindawi Publishing Corporation“]，”type“：”journal“｝，”license“：”抄送人“，”license_id“：”https://openalex.org/licenses/cc-by“，”version“：”publishedVersion“，”is_accepted“：true，”is_published“：true}，”sustainable_development_goals“：[]，”grants“：{”funder“：”https://openalex.org/F4320322795“，”funder_display_name“：”台湾科技部“，”award_id“：”MOST 103-2115-M-029-001“}]，”datasets“：[]，”versions“：[]，”referenced_works_count“：3，”referrenced_works“：[”https://openalex.org/W1976358384","https://openalex.org/W2335389215","https://openalex.org/W2949865692“]，”related_works“：[”https://openalex.org/W4313731559","https://openalex.org/W2544423928","https://openalex.org/W2187401768","https://openalex.org/W2181743346","https://openalex.org/W2181413294","https://openalex.org/W2073681303","https://openalex.org/W2062023542","https://openalex.org/W2053286651","https://openalex.org/W2052122378","https://openalex.org/W2051487156“]，”ngrams_url“：”https://api.openalex.org/works/W2143198086/ngrams“，”abstract_inverted_index“：{”An“(一,秒)-“：[4,13103134]，”顶点反魔“：[5135]，”边缘“：[6,26136]，”标签“：[7118]，”（或“：[8]，”anG公司是“：[20]，”a“：[21,32128152]，”双射“：[22]，”映射“：[23]，”来自“：[24156]，”集合“：[25,36,46,49,73,76,79,86111187]，”E类(G公司)“：[31]”图形的G公司到“：[35]，”set“：[37]，”of“：[38,78,81171175]，”integers1, 2,\2026年,|E类)|带有“：[45]，”属性“：[47]，”that“：[48]，”顶点权重“：[50]，”form“：[51]，”an“：[52140]，”算术“：[53]，”sequence“：[54]，”starting“：55]，”from一和“：[58]，”有“：[59]，”共同“：[60]，”差异秒，”：[63]，“其中一和秒它们是：[68]，“两个”：[69]，“正”：[70]，“整数”，“：[71]，”和“：[72126]，“顶点权重”：[74]，“是”：[75,90154178]，“总和”：[77]，“标签”：[80]，“全部”：[82]，“边”：[83]，“偶发”：[84]，“到”：[85]，“顶点”。“：[87]，”A“：[88]，”图形“：[89153]，”调用)-反魔法“：[95162]，”如果“：[96]，”它“：[97]，”承认“：[98]，”id=\“M13”>(一,1)-VAE“：[117146169]，“disconnected”：[120]，“3-regular”：[121]，“graphs。“：[122]，”另外，“：[123]，”定义“：[125]，”研究“：[127]，”新“：[129]，”概念-->