{"id":"https://openalex.org/W3016910203","doi":"https://doi.org/10.1155/2020/6475427","title":"Game Chromatic Number of Generalized Petersen Graphs and Jahangir Graphs","display_name":"Game Chromatic Number of Generalized Petersen Graphs and Jahangir Graphs","publication_year":2020,"publication_date":"2020-04-14","ids":{"openalex":"https://openalex.org/W3016910203","doi":"https://doi.org/10.1155/2020/6475427","mag":"3016910203"},"language":"en","primary_location":{"id":"doi:10.1155/2020/6475427","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/6475427","pdf_url":"http://downloads.hindawi.com/journals/jam/2020/6475427.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/jam/2020/6475427.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069350357","display_name":"Ramy Shaheen","orcid":"https://orcid.org/0000-0002-8515-6498"},"institutions":[{"id":"https://openalex.org/I108907416","display_name":"Latakia University","ror":"https://ror.org/04nqts970","country_code":"SY","type":"education","lineage":["https://openalex.org/I108907416"]}],"countries":["SY"],"is_corresponding":true,"raw_author_name":"Ramy Shaheen","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria"],"raw_orcid":"https://orcid.org/0000-0002-8515-6498","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria","institution_ids":["https://openalex.org/I108907416"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041337499","display_name":"Ziad Kanaya","orcid":null},"institutions":[{"id":"https://openalex.org/I108907416","display_name":"Latakia University","ror":"https://ror.org/04nqts970","country_code":"SY","type":"education","lineage":["https://openalex.org/I108907416"]}],"countries":["SY"],"is_corresponding":false,"raw_author_name":"Ziad Kanaya","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria","institution_ids":["https://openalex.org/I108907416"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075837468","display_name":"Khaled Alshehada","orcid":null},"institutions":[{"id":"https://openalex.org/I108907416","display_name":"Latakia University","ror":"https://ror.org/04nqts970","country_code":"SY","type":"education","lineage":["https://openalex.org/I108907416"]}],"countries":["SY"],"is_corresponding":false,"raw_author_name":"Khaled Alshehada","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria","institution_ids":["https://openalex.org/I108907416"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5069350357"],"corresponding_institution_ids":["https://openalex.org/I108907416"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06954094,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9984999895095825,"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":0.9984999895095825,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9950000047683716,"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/T11574","display_name":"Artificial Intelligence in Games","score":0.9483000040054321,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.6910182237625122},{"id":"https://openalex.org/keywords/list-coloring","display_name":"List coloring","score":0.6095355153083801},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5268493890762329},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4882643222808838},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.4275832176208496},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3461468517780304},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.07670924067497253}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6910182237625122},{"id":"https://openalex.org/C199594403","wikidata":"https://www.wikidata.org/wiki/Q1130404","display_name":"List coloring","level":5,"score":0.6095355153083801},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5268493890762329},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4882643222808838},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.4275832176208496},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3461468517780304},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.07670924067497253},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2020/6475427","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/6475427","pdf_url":"http://downloads.hindawi.com/journals/jam/2020/6475427.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1589421638","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1589421638","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:6475427","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2020/6475427.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:636ad762faec4e9d98a34d56134ba734","is_oa":true,"landing_page_url":"https://doaj.org/article/636ad762faec4e9d98a34d56134ba734","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2020 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2020/6475427","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/6475427","pdf_url":"http://downloads.hindawi.com/journals/jam/2020/6475427.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320319276","display_name":"Tishreen University","ror":"https://ror.org/04nqts970"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3016910203.pdf","grobid_xml":"https://content.openalex.org/works/W3016910203.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W137844391","https://openalex.org/W1504440667","https://openalex.org/W1973674396","https://openalex.org/W1989513471","https://openalex.org/W1997601467","https://openalex.org/W2011338393","https://openalex.org/W2066808919","https://openalex.org/W2069107705","https://openalex.org/W2108377199","https://openalex.org/W2295838866","https://openalex.org/W2922033540","https://openalex.org/W2954346182","https://openalex.org/W2977851886","https://openalex.org/W2982181498","https://openalex.org/W4230270369","https://openalex.org/W6605667754"],"related_works":["https://openalex.org/W4297911588","https://openalex.org/W2212115383","https://openalex.org/W2546620014","https://openalex.org/W2793500002","https://openalex.org/W4291316360","https://openalex.org/W2380525562","https://openalex.org/W2585997002","https://openalex.org/W4380300356","https://openalex.org/W3169197204","https://openalex.org/W4311345810"],"abstract_inverted_index":{"Let":[0],"<a:math":[1],"xmlns:a=\"http://www.w3.org/1998/Math/MathML\"":[2],"id=\"M1\">":[3],"<a:mi>G</a:mi>":[4],"<a:mo>=</a:mo>":[5],"<a:mfenced":[6],"open=\"(\"":[7,90,128,146],"close=\")\"":[8,91,129,147],"separators=\"|\">":[9,92,130,148],"<a:mrow>":[10],"<a:mi>V</a:mi>":[11],"<a:mo>,</a:mo>":[12],"<a:mi>E</a:mi>":[13],"</a:mrow>":[14],"</a:mfenced>":[15],"</a:math>":[16],"be":[17],"a":[18,39],"graph,":[19],"and":[20,24,74,164,180],"two":[21,44],"players":[22],"Alice":[23],"Bob":[25],"alternate":[26],"turns":[27],"coloring":[28,41],"the":[29,32,50,58,63,112],"vertices":[30,46,61],"of":[31,60,66,136],"graph":[33],"<f:math":[34],"xmlns:f=\"http://www.w3.org/1998/Math/MathML\"":[35],"id=\"M2\">":[36],"<f:mi>G</f:mi>":[37],"</f:math>":[38],"proper":[40],"where":[42],"no":[43],"adjacent":[45],"are":[47],"signed":[48],"with":[49],"same":[51],"color.":[52],"Alice's":[53,105],"goal":[54,101],"is":[55,69,75,102],"to":[56,103],"color":[57],"set":[59],"using":[62],"minimum":[64],"number":[65,73,115],"colors,":[67],"which":[68],"called":[70],"game":[71,113],"chromatic":[72,114],"denoted":[76],"by":[77],"<h:math":[78],"xmlns:h=\"http://www.w3.org/1998/Math/MathML\"":[79],"id=\"M3\">":[80],"<h:msub>":[81],"<h:mrow>":[82,85,93],"<h:mi>\u03c7</h:mi>":[83],"</h:mrow>":[84,87,95],"<h:mi>g</h:mi>":[86],"</h:msub>":[88],"<h:mfenced":[89],"<h:mi>G</h:mi>":[94],"</h:mfenced>":[96],"</h:math>":[97],",":[98,171],"while":[99],"Bob's":[100],"prevent":[104],"goal.":[106],"In":[107],"this":[108],"paper,":[109],"we":[110],"investigate":[111],"<m:math":[116],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\"":[117],"id=\"M4\">":[118],"<m:msub>":[119],"<m:mrow>":[120,123,131],"<m:mi>\u03c7</m:mi>":[121],"</m:mrow>":[122,125,133],"<m:mi>g</m:mi>":[124],"</m:msub>":[126],"<m:mfenced":[127],"<m:mi>G</m:mi>":[132],"</m:mfenced>":[134],"</m:math>":[135],"Generalized":[137],"Petersen":[138],"Graphs":[139],"<r:math":[140],"xmlns:r=\"http://www.w3.org/1998/Math/MathML\"":[141],"id=\"M5\">":[142],"<r:mi>G</r:mi>":[143],"<r:mi>P</r:mi>":[144],"<r:mfenced":[145],"<r:mrow>":[149],"<r:mi>n</r:mi>":[150],"<r:mo>,</r:mo>":[151],"<r:mi>k</r:mi>":[152],"</r:mrow>":[153],"</r:mfenced>":[154],"</r:math>":[155],"for":[156],"<w:math":[157],"xmlns:w=\"http://www.w3.org/1998/Math/MathML\"":[158],"id=\"M6\">":[159],"<w:mi>k</w:mi>":[160],"<w:mo>\u2265</w:mo>":[161],"<w:mn>3</w:mn>":[162],"</w:math>":[163],"arbitrary":[165],"<y:math":[166],"xmlns:y=\"http://www.w3.org/1998/Math/MathML\"":[167],"id=\"M7\">":[168],"<y:mi>n</y:mi>":[169],"</y:math>":[170],"<ab:math":[172],"xmlns:ab=\"http://www.w3.org/1998/Math/MathML\"":[173],"id=\"M8\">":[174],"<ab:mi>n</ab:mi>":[175],"</ab:math>":[176],"-Crossed":[177],"Prism":[178],"Graph,":[179],"Jahangir":[181],"Graph":[182],"<cb:math":[183],"xmlns:cb=\"http://www.w3.org/1998/Math/MathML\"":[184],"id=\"M9\">":[185],"<cb:msub>":[186],"<cb:mrow>":[187,190],"<cb:mi>J</cb:mi>":[188],"</cb:mrow>":[189,194],"<cb:mi>n</cb:mi>":[191],"<cb:mo>,</cb:mo>":[192],"<cb:mi>m</cb:mi>":[193],"</cb:msub>":[195],"</cb:math>":[196],".":[197]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
