{"title":"二面体群的Cayley图的可靠性分析*","authors":"Song Shujiao (宋淑娇), Wang Dianjun (王殿军)","doi":"10.1016/S1007-0214(11)70006-2","DOIUrl":null,"url":null,"abstract":"<div><p>Cayley graphs have many good properties as models of communication networks. This study analyzes the reliability of the Cayley graph based on the dihedral graph. Graph theory and analyses show that almost all Cayley graphs of the dihedral graph <em>D</em><sub>2<em>n</em></sub> are optimal super-λ. The number <em>N<sub>i</sub>(G)</em> of cutsets of size <em>i</em>,λ≤<em>i</em>≤λ′ is given as\n<span><math><mrow><msub><mi>N</mi><mi>i</mi></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>n</mi><mrow><mo>(</mo><mrow><mtable><mtr><mtd><mrow><mo>(</mo><mi>G</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><mi>i</mi><mo>−</mo><mi>δ</mi></mrow></mtd></mtr></mtable></mrow><mo>)</mo></mrow><mo>.</mo></mrow></math></span></p></div>","PeriodicalId":60306,"journal":{"name":"Tsinghua Science and Technology","volume":null,"pages":null},"PeriodicalIF":5.2000,"publicationDate":"2011-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1007-0214(11)70006-2","citationCount":"1","resultStr":"{\"title\":\"Reliability Analysis of the Cayley Graphs of Dihedral Groups*\",\"authors\":\"Song Shujiao (宋淑娇), Wang Dianjun (王殿军)\",\"doi\":\"10.1016/S1007-0214(11)70006-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Cayley graphs have many good properties as models of communication networks. This study analyzes the reliability of the Cayley graph based on the dihedral graph. Graph theory and analyses show that almost all Cayley graphs of the dihedral graph <em>D</em><sub>2<em>n</em></sub> are optimal super-λ. The number <em>N<sub>i</sub>(G)</em> of cutsets of size <em>i</em>,λ≤<em>i</em>≤λ′ is given as\\n<span><math><mrow><msub><mi>N</mi><mi>i</mi></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>n</mi><mrow><mo>(</mo><mrow><mtable><mtr><mtd><mrow><mo>(</mo><mi>G</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><mi>i</mi><mo>−</mo><mi>δ</mi></mrow></mtd></mtr></mtable></mrow><mo>)</mo></mrow><mo>.</mo></mrow></math></span></p></div>\",\"PeriodicalId\":60306,\"journal\":{\"name\":\"Tsinghua Science and Technology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":5.2000,\"publicationDate\":\"2011-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1007-0214(11)70006-2\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tsinghua Science and Technology\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1007021411700062\",\"RegionNum\":1,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, INFORMATION SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsinghua Science and Technology","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007021411700062","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
Reliability Analysis of the Cayley Graphs of Dihedral Groups*
Cayley graphs have many good properties as models of communication networks. This study analyzes the reliability of the Cayley graph based on the dihedral graph. Graph theory and analyses show that almost all Cayley graphs of the dihedral graph D2n are optimal super-λ. The number Ni(G) of cutsets of size i,λ≤i≤λ′ is given as
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