{"title":"图形中的拆分迂回单音集","authors":"M. Mahendran, R. Kavitha","doi":"10.37394/23205.2024.23.5","DOIUrl":null,"url":null,"abstract":"A subset T ⊆ V is a detourmonophonic set of G if each node (vertex) x in G contained in an p-q detourmonophonic path where p, q ∈ T.. The number of points in a minimum detourmonophonic set of G is called as the detourmonophonic number of G, dm(G). A subset T ⊆ V of a connected graph G is said to be a split detourmonophonic set of G if the set T of vertices is either T = V or T is detoumonophonic set and V – T induces a subgraph in which is disconnected. The minimum split detourmonophonic set is split detourmonophonic set with minimum cardinality and it is called a split detourmonophonic number, denoted by dms(G). For certain standard graphs, defined new parameter was identified. Some of the realization results on defined new parameters were established.","PeriodicalId":332148,"journal":{"name":"WSEAS TRANSACTIONS ON COMPUTERS","volume":"111 13","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Split Detour Monophonic Sets in Graph\",\"authors\":\"M. Mahendran, R. Kavitha\",\"doi\":\"10.37394/23205.2024.23.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A subset T ⊆ V is a detourmonophonic set of G if each node (vertex) x in G contained in an p-q detourmonophonic path where p, q ∈ T.. The number of points in a minimum detourmonophonic set of G is called as the detourmonophonic number of G, dm(G). A subset T ⊆ V of a connected graph G is said to be a split detourmonophonic set of G if the set T of vertices is either T = V or T is detoumonophonic set and V – T induces a subgraph in which is disconnected. The minimum split detourmonophonic set is split detourmonophonic set with minimum cardinality and it is called a split detourmonophonic number, denoted by dms(G). For certain standard graphs, defined new parameter was identified. Some of the realization results on defined new parameters were established.\",\"PeriodicalId\":332148,\"journal\":{\"name\":\"WSEAS TRANSACTIONS ON COMPUTERS\",\"volume\":\"111 13\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"WSEAS TRANSACTIONS ON COMPUTERS\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37394/23205.2024.23.5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS TRANSACTIONS ON COMPUTERS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/23205.2024.23.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
如果 G 中的每个节点(顶点)x 都包含在一条 pq 非单音路径中(其中 p,q∈T),则子集 T ⊆ V 是 G 的非单音集合。G 的最小失谐集合中的点数称为 G 的失谐数 dm(G)。如果顶点集 T 要么是 T = V,要么 T 是去单音集,并且 V - T 引发了一个断开的子图,则称连通图 G 的子集 T ⊆ V 为 G 的分裂去单音集。最小分裂失单音集是具有最小心数的分裂失单音集,称为分裂失单音数,用 dms(G) 表示。对于某些标准图形,确定了定义的新参数。建立了一些关于定义新参数的实现结果。
A subset T ⊆ V is a detourmonophonic set of G if each node (vertex) x in G contained in an p-q detourmonophonic path where p, q ∈ T.. The number of points in a minimum detourmonophonic set of G is called as the detourmonophonic number of G, dm(G). A subset T ⊆ V of a connected graph G is said to be a split detourmonophonic set of G if the set T of vertices is either T = V or T is detoumonophonic set and V – T induces a subgraph in which is disconnected. The minimum split detourmonophonic set is split detourmonophonic set with minimum cardinality and it is called a split detourmonophonic number, denoted by dms(G). For certain standard graphs, defined new parameter was identified. Some of the realization results on defined new parameters were established.