{"title":"带边缘断层的莫比乌斯立方体的全循环性","authors":"S. Hsieh, Chun-Hua Chen","doi":"10.1109/ISPAN.2004.1300476","DOIUrl":null,"url":null,"abstract":"A graph G = (V, E) is said to be pancyclic if it contains cycles of all lengths from 4 to |V| in G. Let F/sub e/ be the set of faulty edges. In this paper, we show that an n-dimensional Mobius cube, n /spl ges/ 1, contains a fault-free Hamiltonian path when |F/sub e/| /spl les/ n-1. We also show that an n-dimensional Mobius cube, n /spl ges/ 2, is pancyclic when |F/sub e/| /spl les/ n-2. Since an n-dimensional Mobius cube is regular of degree n, both results are optimal in the worst case.","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":"0","resultStr":"{\"title\":\"Pancyclicity on Mobius cubes with edge faults\",\"authors\":\"S. Hsieh, Chun-Hua Chen\",\"doi\":\"10.1109/ISPAN.2004.1300476\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A graph G = (V, E) is said to be pancyclic if it contains cycles of all lengths from 4 to |V| in G. Let F/sub e/ be the set of faulty edges. In this paper, we show that an n-dimensional Mobius cube, n /spl ges/ 1, contains a fault-free Hamiltonian path when |F/sub e/| /spl les/ n-1. We also show that an n-dimensional Mobius cube, n /spl ges/ 2, is pancyclic when |F/sub e/| /spl les/ n-2. Since an n-dimensional Mobius cube is regular of degree n, both results are optimal in the worst case.\",\"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\":\"0\",\"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.2004.1300476\",\"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.2004.1300476","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A graph G = (V, E) is said to be pancyclic if it contains cycles of all lengths from 4 to |V| in G. Let F/sub e/ be the set of faulty edges. In this paper, we show that an n-dimensional Mobius cube, n /spl ges/ 1, contains a fault-free Hamiltonian path when |F/sub e/| /spl les/ n-1. We also show that an n-dimensional Mobius cube, n /spl ges/ 2, is pancyclic when |F/sub e/| /spl les/ n-2. Since an n-dimensional Mobius cube is regular of degree n, both results are optimal in the worst case.
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