{"title":"关于共隔离图","authors":"T. F. Jorry","doi":"10.17654/0974165823011","DOIUrl":null,"url":null,"abstract":"A connected graph G is totally segregated if every pair of adjacent vertices has distinct degrees. In this article, the class of graphs called co-segregated graphs which are complements of totally segregated graphs is discussed. The maximum size of connected totally segregated graph is found by finding minimum size of a large class of co-segregated graphs. We provide an algorithm to find minimum size of co-segregated graph. A construction of co-segregated graph of order n with minimum size is also described.","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON CO-SEGREGATED GRAPHS\",\"authors\":\"T. F. Jorry\",\"doi\":\"10.17654/0974165823011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A connected graph G is totally segregated if every pair of adjacent vertices has distinct degrees. In this article, the class of graphs called co-segregated graphs which are complements of totally segregated graphs is discussed. The maximum size of connected totally segregated graph is found by finding minimum size of a large class of co-segregated graphs. We provide an algorithm to find minimum size of co-segregated graph. A construction of co-segregated graph of order n with minimum size is also described.\",\"PeriodicalId\":40868,\"journal\":{\"name\":\"Advances and Applications in Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-01-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances and Applications in Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17654/0974165823011\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances and Applications in Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17654/0974165823011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
A connected graph G is totally segregated if every pair of adjacent vertices has distinct degrees. In this article, the class of graphs called co-segregated graphs which are complements of totally segregated graphs is discussed. The maximum size of connected totally segregated graph is found by finding minimum size of a large class of co-segregated graphs. We provide an algorithm to find minimum size of co-segregated graph. A construction of co-segregated graph of order n with minimum size is also described.
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