{"title":"关于二进制交换有限网络","authors":"Tao Yu, Xingxing Zhou, Chang-Qing Xu","doi":"10.1109/WCICA.2012.6359211","DOIUrl":null,"url":null,"abstract":"We call a finite graph G = (V, E) a binary network if the state set of its nodes has only two elements,say, 0 and 1, representing respectively 'OFF' and 'ON' state. A switch at node v switches both the state of v and the state of each of its neighbors. It is shown in [1] that given any initial state of a network of order n >; 3, we can always reach at a consistent status, i.e., either all the nodes are ON or all are OFF. In this paper we consider a more general problem: Given a subset S ⊂ V , can we reach to a state such that the state of each node within S is 1(or 0) while the states of nodes outside S is another? We present some sufficient conditions for some specific S that satisfies this condition.","PeriodicalId":114901,"journal":{"name":"Proceedings of the 10th World Congress on Intelligent Control and Automation","volume":"46 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On binary switching finite networks\",\"authors\":\"Tao Yu, Xingxing Zhou, Chang-Qing Xu\",\"doi\":\"10.1109/WCICA.2012.6359211\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We call a finite graph G = (V, E) a binary network if the state set of its nodes has only two elements,say, 0 and 1, representing respectively 'OFF' and 'ON' state. A switch at node v switches both the state of v and the state of each of its neighbors. It is shown in [1] that given any initial state of a network of order n >; 3, we can always reach at a consistent status, i.e., either all the nodes are ON or all are OFF. In this paper we consider a more general problem: Given a subset S ⊂ V , can we reach to a state such that the state of each node within S is 1(or 0) while the states of nodes outside S is another? We present some sufficient conditions for some specific S that satisfies this condition.\",\"PeriodicalId\":114901,\"journal\":{\"name\":\"Proceedings of the 10th World Congress on Intelligent Control and Automation\",\"volume\":\"46 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-07-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 10th World Congress on Intelligent Control and Automation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/WCICA.2012.6359211\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 10th World Congress on Intelligent Control and Automation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/WCICA.2012.6359211","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We call a finite graph G = (V, E) a binary network if the state set of its nodes has only two elements,say, 0 and 1, representing respectively 'OFF' and 'ON' state. A switch at node v switches both the state of v and the state of each of its neighbors. It is shown in [1] that given any initial state of a network of order n >; 3, we can always reach at a consistent status, i.e., either all the nodes are ON or all are OFF. In this paper we consider a more general problem: Given a subset S ⊂ V , can we reach to a state such that the state of each node within S is 1(or 0) while the states of nodes outside S is another? We present some sufficient conditions for some specific S that satisfies this condition.
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