Cheng-Kuan Lin, Hua-Min Huang, D. Hsu, Lih-Hsing Hsu
{"title":"星图的张成直径","authors":"Cheng-Kuan Lin, Hua-Min Huang, D. Hsu, Lih-Hsing Hsu","doi":"10.1109/ISPAN.2004.1300536","DOIUrl":null,"url":null,"abstract":"Assume that u and v are any two distinct vertices of different partite sets of S/sub n/ with n /spl ges/ 5. We prove that there are (n - 1) internally disjoint paths P/sub 1/, P/sub 2/, ..., P/sub n-i/ joining u to v such that /spl cup//sup n = 1//sub i = 2/ P/sub i/ spans S/sub n/ and l(P/sub i/) /spl les/ (n - 1)! + 2(n - 2)! + 2(n - 3)! + 1 = n!/(n - 2) + 1. We also prove that there are two internally disjoint paths Q/sub 1/ and Q/sub 2/ joining u to v such that Q/sub 1/ /spl cup/ Q/sub 2/ spans S/sub n/ and l(Q/sub i/) /spl les/ n!/2 + l for i = 1,2.","PeriodicalId":198404,"journal":{"name":"7th International Symposium on Parallel Architectures, Algorithms and Networks, 2004. Proceedings.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2004-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"The spanning diameter of the star graphs\",\"authors\":\"Cheng-Kuan Lin, Hua-Min Huang, D. Hsu, Lih-Hsing Hsu\",\"doi\":\"10.1109/ISPAN.2004.1300536\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Assume that u and v are any two distinct vertices of different partite sets of S/sub n/ with n /spl ges/ 5. We prove that there are (n - 1) internally disjoint paths P/sub 1/, P/sub 2/, ..., P/sub n-i/ joining u to v such that /spl cup//sup n = 1//sub i = 2/ P/sub i/ spans S/sub n/ and l(P/sub i/) /spl les/ (n - 1)! + 2(n - 2)! + 2(n - 3)! + 1 = n!/(n - 2) + 1. We also prove that there are two internally disjoint paths Q/sub 1/ and Q/sub 2/ joining u to v such that Q/sub 1/ /spl cup/ Q/sub 2/ spans S/sub n/ and l(Q/sub i/) /spl les/ n!/2 + l for i = 1,2.\",\"PeriodicalId\":198404,\"journal\":{\"name\":\"7th International Symposium on Parallel Architectures, Algorithms and Networks, 2004. Proceedings.\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"7th International Symposium on Parallel Architectures, Algorithms and Networks, 2004. Proceedings.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISPAN.2004.1300536\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"7th International Symposium on Parallel Architectures, Algorithms and Networks, 2004. Proceedings.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISPAN.2004.1300536","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Assume that u and v are any two distinct vertices of different partite sets of S/sub n/ with n /spl ges/ 5. We prove that there are (n - 1) internally disjoint paths P/sub 1/, P/sub 2/, ..., P/sub n-i/ joining u to v such that /spl cup//sup n = 1//sub i = 2/ P/sub i/ spans S/sub n/ and l(P/sub i/) /spl les/ (n - 1)! + 2(n - 2)! + 2(n - 3)! + 1 = n!/(n - 2) + 1. We also prove that there are two internally disjoint paths Q/sub 1/ and Q/sub 2/ joining u to v such that Q/sub 1/ /spl cup/ Q/sub 2/ spans S/sub n/ and l(Q/sub i/) /spl les/ n!/2 + l for i = 1,2.