{"title":"由循环图和一分解图的若干副本构成的完全二部图的正交重盖","authors":"R. El-Shanawany, E. El-Kholy, T. Homoda, Z. Bakr","doi":"10.1109/ICEEM52022.2021.9480658","DOIUrl":null,"url":null,"abstract":"Let K<inf>n,n</inf> be a complete bipartite graph on 2n vertices and G be a collection of 2n subgraphs of K<inf>n,n</inf>, then G is an orthogonal double cover (ODC) of K<inf>n,n</inf> if every edge of K<inf>n,n</inf> exists in exactly two members of G and any two members of G share exactly an edge. If all subgraphs in G are isomorphic to a given subgraph G, then G is said to be an ODC of K<inf>n,n</inf> by G. Our aim is to get an ODC of K<inf>n,n</inf> by ∪C<inf>s</inf>; s < n, and we will make extension for this ODC to get another one of K<inf>m,m</inf> by ∪(αC<inf>s</inf>); where m = αn; α ∈ Z<sup>+</sup>.","PeriodicalId":352371,"journal":{"name":"2021 International Conference on Electronic Engineering (ICEEM)","volume":"223 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Orthogonal Double Covers of Complete Bipartite Graphs by Certain Copies of Cyclic and one Factorization Graphs\",\"authors\":\"R. El-Shanawany, E. El-Kholy, T. Homoda, Z. Bakr\",\"doi\":\"10.1109/ICEEM52022.2021.9480658\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let K<inf>n,n</inf> be a complete bipartite graph on 2n vertices and G be a collection of 2n subgraphs of K<inf>n,n</inf>, then G is an orthogonal double cover (ODC) of K<inf>n,n</inf> if every edge of K<inf>n,n</inf> exists in exactly two members of G and any two members of G share exactly an edge. If all subgraphs in G are isomorphic to a given subgraph G, then G is said to be an ODC of K<inf>n,n</inf> by G. Our aim is to get an ODC of K<inf>n,n</inf> by ∪C<inf>s</inf>; s < n, and we will make extension for this ODC to get another one of K<inf>m,m</inf> by ∪(αC<inf>s</inf>); where m = αn; α ∈ Z<sup>+</sup>.\",\"PeriodicalId\":352371,\"journal\":{\"name\":\"2021 International Conference on Electronic Engineering (ICEEM)\",\"volume\":\"223 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2021 International Conference on Electronic Engineering (ICEEM)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICEEM52022.2021.9480658\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 International Conference on Electronic Engineering (ICEEM)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICEEM52022.2021.9480658","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Orthogonal Double Covers of Complete Bipartite Graphs by Certain Copies of Cyclic and one Factorization Graphs
Let Kn,n be a complete bipartite graph on 2n vertices and G be a collection of 2n subgraphs of Kn,n, then G is an orthogonal double cover (ODC) of Kn,n if every edge of Kn,n exists in exactly two members of G and any two members of G share exactly an edge. If all subgraphs in G are isomorphic to a given subgraph G, then G is said to be an ODC of Kn,n by G. Our aim is to get an ODC of Kn,n by ∪Cs; s < n, and we will make extension for this ODC to get another one of Km,m by ∪(αCs); where m = αn; α ∈ Z+.
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