{"title":"调换树生成的Cayley图的(E)FTSM-(边)连通性","authors":"Pingshan Li, Rong Liu, Xianglin Liu","doi":"10.1142/s0129054121500349","DOIUrl":null,"url":null,"abstract":"The Cayley graph generated by a transposition tree [Formula: see text] is a class of Cayley graphs that contains the star graph and the bubble sort graph. A graph [Formula: see text] is called strongly Menger (SM for short) (edge) connected if each pair of vertices [Formula: see text] are connected by [Formula: see text] (edge)-disjoint paths, where [Formula: see text] are the degree of [Formula: see text] and [Formula: see text] respectively. In this paper, the maximally edge-fault-tolerant and the maximally vertex-fault-tolerant of [Formula: see text] with respect to the SM-property are found and thus generalize or improve the results in [19, 20, 22, 26] on this topic.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The (E)FTSM-(edge) Connectivity of Cayley Graphs Generated by Transposition Trees\",\"authors\":\"Pingshan Li, Rong Liu, Xianglin Liu\",\"doi\":\"10.1142/s0129054121500349\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Cayley graph generated by a transposition tree [Formula: see text] is a class of Cayley graphs that contains the star graph and the bubble sort graph. A graph [Formula: see text] is called strongly Menger (SM for short) (edge) connected if each pair of vertices [Formula: see text] are connected by [Formula: see text] (edge)-disjoint paths, where [Formula: see text] are the degree of [Formula: see text] and [Formula: see text] respectively. In this paper, the maximally edge-fault-tolerant and the maximally vertex-fault-tolerant of [Formula: see text] with respect to the SM-property are found and thus generalize or improve the results in [19, 20, 22, 26] on this topic.\",\"PeriodicalId\":192109,\"journal\":{\"name\":\"Int. J. Found. Comput. Sci.\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-10-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Int. J. Found. Comput. Sci.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0129054121500349\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Found. Comput. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0129054121500349","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The (E)FTSM-(edge) Connectivity of Cayley Graphs Generated by Transposition Trees
The Cayley graph generated by a transposition tree [Formula: see text] is a class of Cayley graphs that contains the star graph and the bubble sort graph. A graph [Formula: see text] is called strongly Menger (SM for short) (edge) connected if each pair of vertices [Formula: see text] are connected by [Formula: see text] (edge)-disjoint paths, where [Formula: see text] are the degree of [Formula: see text] and [Formula: see text] respectively. In this paper, the maximally edge-fault-tolerant and the maximally vertex-fault-tolerant of [Formula: see text] with respect to the SM-property are found and thus generalize or improve the results in [19, 20, 22, 26] on this topic.
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