{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:38:04Z","timestamp":1747190284840,"version":"3.40.5"},"reference-count":15,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T00:00:00Z","timestamp":1586822400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Tishreen University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2020,4,14]]},"abstract":"<jats:p>Let <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                        <a:mi>G<\/a:mi>\n                        <a:mo>=<\/a:mo>\n                        <a:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <a:mrow>\n                              <a:mi>V<\/a:mi>\n                              <a:mo>,<\/a:mo>\n                              <a:mi>E<\/a:mi>\n                           <\/a:mrow>\n                        <\/a:mfenced>\n                     <\/a:math>\n                  <\/jats:inline-formula> be a graph, and two players Alice and Bob alternate turns coloring the vertices of the graph <jats:inline-formula>\n                     <f:math xmlns:f=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <f:mi>G<\/f:mi>\n                     <\/f:math>\n                  <\/jats:inline-formula> a proper coloring where no two adjacent vertices are signed with the same color. Alice's goal is to color the set of vertices using the minimum number of colors, which is called game chromatic number and is denoted by <jats:inline-formula>\n                     <h:math xmlns:h=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <h:msub>\n                           <h:mrow>\n                              <h:mi>\u03c7<\/h:mi>\n                           <\/h:mrow>\n                           <h:mrow>\n                              <h:mi>g<\/h:mi>\n                           <\/h:mrow>\n                        <\/h:msub>\n                        <h:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <h:mrow>\n                              <h:mi>G<\/h:mi>\n                           <\/h:mrow>\n                        <\/h:mfenced>\n                     <\/h:math>\n                  <\/jats:inline-formula>, while Bob's goal is to prevent Alice's goal. In this paper, we investigate the game chromatic number <jats:inline-formula>\n                     <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <m:msub>\n                           <m:mrow>\n                              <m:mi>\u03c7<\/m:mi>\n                           <\/m:mrow>\n                           <m:mrow>\n                              <m:mi>g<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:msub>\n                        <m:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <m:mrow>\n                              <m:mi>G<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:mfenced>\n                     <\/m:math>\n                  <\/jats:inline-formula> of Generalized Petersen Graphs <jats:inline-formula>\n                     <r:math xmlns:r=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\">\n                        <r:mi>G<\/r:mi>\n                        <r:mi>P<\/r:mi>\n                        <r:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <r:mrow>\n                              <r:mi>n<\/r:mi>\n                              <r:mo>,<\/r:mo>\n                              <r:mi>k<\/r:mi>\n                           <\/r:mrow>\n                        <\/r:mfenced>\n                     <\/r:math>\n                  <\/jats:inline-formula> for <jats:inline-formula>\n                     <w:math xmlns:w=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\">\n                        <w:mi>k<\/w:mi>\n                        <w:mo>\u2265<\/w:mo>\n                        <w:mn>3<\/w:mn>\n                     <\/w:math>\n                  <\/jats:inline-formula> and arbitrary <jats:inline-formula>\n                     <y:math xmlns:y=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\">\n                        <y:mi>n<\/y:mi>\n                     <\/y:math>\n                  <\/jats:inline-formula>, <jats:inline-formula>\n                     <ab:math xmlns:ab=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\">\n                        <ab:mi>n<\/ab:mi>\n                     <\/ab:math>\n                  <\/jats:inline-formula>-Crossed Prism Graph, and Jahangir Graph <jats:inline-formula>\n                     <cb:math xmlns:cb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\">\n                        <cb:msub>\n                           <cb:mrow>\n                              <cb:mi>J<\/cb:mi>\n                           <\/cb:mrow>\n                           <cb:mrow>\n                              <cb:mi>n<\/cb:mi>\n                              <cb:mo>,<\/cb:mo>\n                              <cb:mi>m<\/cb:mi>\n                           <\/cb:mrow>\n                        <\/cb:msub>\n                     <\/cb:math>\n                  <\/jats:inline-formula>.<\/jats:p>","DOI":"10.1155\/2020\/6475427","type":"journal-article","created":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T23:32:43Z","timestamp":1586907163000},"page":"1-4","source":"Crossref","is-referenced-by-count":0,"title":["Game Chromatic Number of Generalized Petersen Graphs and Jahangir Graphs"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8515-6498","authenticated-orcid":true,"given":"Ramy","family":"Shaheen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria"}]},{"given":"Ziad","family":"Kanaya","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria"}]},{"given":"Khaled","family":"Alshehada","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.2007.11920471"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(92)90254-D"},{"key":"3","first-page":"143","article-title":"On the game chromatic number of some classes of graphs","volume":"35","author":"U. 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Akhtar","year":"2019","journal-title":"Theoretical Computer Science"},{"key":"14","first-page":"17","article-title":"On game chromatic number analogues of Mycielsians and Brooks\u2019 Theorem","volume":"5","author":"C. Chamberlin","year":"2019","journal-title":"North Carolina Journal of Mathematics and Statistics"},{"volume-title":"The Game Chromatic Number of Some Classes of Graphs, DLSU Research Congress","year":"2014","author":"C. J. Destacamento","key":"15"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2020\/6475427.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2020\/6475427.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2020\/6475427.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,19]],"date-time":"2020-10-19T15:17:47Z","timestamp":1603120667000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/jam\/2020\/6475427\/"}},"subtitle":[],"editor":[{"given":"Kannan","family":"Krithivasan","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2020,4,14]]},"references-count":15,"alternative-id":["6475427","6475427"],"URL":"https:\/\/doi.org\/10.1155\/2020\/6475427","relation":{},"ISSN":["1687-0042","1110-757X"],"issn-type":[{"type":"electronic","value":"1687-0042"},{"type":"print","value":"1110-757X"}],"subject":[],"published":{"date-parts":[[2020,4,14]]}}}