完全图分解为八边五边形连通单环图

Indonesian Journal of Combinatorics Pub Date : 2019-06-30 DOI:10.19184/IJC.2019.3.1.3

D. Froncek, O'Neill Kingston

{"title":"完全图分解为八边五边形连通单环图","authors":"D. Froncek, O'Neill Kingston","doi":"10.19184/IJC.2019.3.1.3","DOIUrl":null,"url":null,"abstract":"A G-decomposition of the complete graph Kn is a family of pairwise edge disjoint subgraphs of Kn, all isomorphic to G, such that every edge of Kn belongs to exactly one copy of G. Using standard decomposition techniques based on ρ-labelings, introduced by Rosa in 1967, and their modifications we show that each of the ten non-isomorphic connected unicyclic graphs with eight edges containing the pentagon decomposes the complete graph Kn whenever the necessary conditions are satisfied.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Decomposition of complete graphs into connected unicyclic graphs with eight edges and pentagon\",\"authors\":\"D. Froncek, O'Neill Kingston\",\"doi\":\"10.19184/IJC.2019.3.1.3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A G-decomposition of the complete graph Kn is a family of pairwise edge disjoint subgraphs of Kn, all isomorphic to G, such that every edge of Kn belongs to exactly one copy of G. Using standard decomposition techniques based on ρ-labelings, introduced by Rosa in 1967, and their modifications we show that each of the ten non-isomorphic connected unicyclic graphs with eight edges containing the pentagon decomposes the complete graph Kn whenever the necessary conditions are satisfied.\",\"PeriodicalId\":13506,\"journal\":{\"name\":\"Indonesian Journal of Combinatorics\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indonesian Journal of Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.19184/IJC.2019.3.1.3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indonesian Journal of Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.19184/IJC.2019.3.1.3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 2

摘要

完全图Kn的G分解是Kn的一对边不相交子图族，它们都与G同构，使得Kn的每条边都属于G的一个副本。利用1967年由Rosa引入的基于ρ-标记的标准分解技术及其修正，我们证明了只要满足必要条件，10个有8条边包含五边形的非同构连通单环图中的每一个都分解了完全图Kn。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Decomposition of complete graphs into connected unicyclic graphs with eight edges and pentagon

A G-decomposition of the complete graph K_n is a family of pairwise edge disjoint subgraphs of K_n, all isomorphic to G, such that every edge of K_n belongs to exactly one copy of G. Using standard decomposition techniques based on ρ-labelings, introduced by Rosa in 1967, and their modifications we show that each of the ten non-isomorphic connected unicyclic graphs with eight edges containing the pentagon decomposes the complete graph K_n whenever the necessary conditions are satisfied.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Indonesian Journal of Combinatorics

自引率

0.00%

发文量

期刊最新文献

A note on vertex irregular total labeling of trees On Ramsey (mK2,bPn)-minimal Graphs Local Strong Rainbow Connection Number of Corona Product Between Cycle Graphs Γ-supermagic labeling of products of two cycles with cyclic groups On graphs associated to topological spaces