{"title":"关于相互正交的图路径平方","authors":"R. El-Shanawany","doi":"10.4236/OJDM.2016.61002","DOIUrl":null,"url":null,"abstract":"A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G. Two decompositions and of the complete bipartite graph are orthogonal if, for all . A set of decompositions of is a set of k mutually orthogonal graph squares (MOGS) if and are orthogonal for all and . For any bipartite graph G with n edges, denotes the maximum number k in a largest possible set of MOGS of by G. Our objective in this paper is to compute where is a path of length d with d + 1 vertices (i.e. Every edge of this path is one-to-one corresponding to an isomorphic to a certain graph F).","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"51 1","pages":"7-12"},"PeriodicalIF":0.0000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"On Mutually Orthogonal Graph-Path Squares\",\"authors\":\"R. El-Shanawany\",\"doi\":\"10.4236/OJDM.2016.61002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G. Two decompositions and of the complete bipartite graph are orthogonal if, for all . A set of decompositions of is a set of k mutually orthogonal graph squares (MOGS) if and are orthogonal for all and . For any bipartite graph G with n edges, denotes the maximum number k in a largest possible set of MOGS of by G. Our objective in this paper is to compute where is a path of length d with d + 1 vertices (i.e. Every edge of this path is one-to-one corresponding to an isomorphic to a certain graph F).\",\"PeriodicalId\":61712,\"journal\":{\"name\":\"离散数学期刊(英文)\",\"volume\":\"51 1\",\"pages\":\"7-12\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"离散数学期刊(英文)\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.4236/OJDM.2016.61002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"离散数学期刊(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/OJDM.2016.61002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G. Two decompositions and of the complete bipartite graph are orthogonal if, for all . A set of decompositions of is a set of k mutually orthogonal graph squares (MOGS) if and are orthogonal for all and . For any bipartite graph G with n edges, denotes the maximum number k in a largest possible set of MOGS of by G. Our objective in this paper is to compute where is a path of length d with d + 1 vertices (i.e. Every edge of this path is one-to-one corresponding to an isomorphic to a certain graph F).
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