{"title":"最多有两个循环的连通图中最大独立集数的另一种证明","authors":"Min-Jen Jou, Jenq-Jong Lin","doi":"10.4236/OJDM.2016.64019","DOIUrl":null,"url":null,"abstract":"G. C. Ying, Y. Y. Meng, B. E. Sagan, and V. R. Vatter [1] found the maximum number of maximal independent sets in connected graphs which contain at most two cycles. In this paper, we give an alternative proof to determine the largest number of maximal independent sets among all connected graphs of order n ≥ 12, which contain at most two cycles. We also characterize the extremal graph achieving this maximum value.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"227-237"},"PeriodicalIF":0.0000,"publicationDate":"2016-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"An Alternative Proof of the Largest Number of Maximal Independent Sets in Connected Graphs Having at Most Two Cycles\",\"authors\":\"Min-Jen Jou, Jenq-Jong Lin\",\"doi\":\"10.4236/OJDM.2016.64019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"G. C. Ying, Y. Y. Meng, B. E. Sagan, and V. R. Vatter [1] found the maximum number of maximal independent sets in connected graphs which contain at most two cycles. In this paper, we give an alternative proof to determine the largest number of maximal independent sets among all connected graphs of order n ≥ 12, which contain at most two cycles. We also characterize the extremal graph achieving this maximum value.\",\"PeriodicalId\":61712,\"journal\":{\"name\":\"离散数学期刊(英文)\",\"volume\":\"06 1\",\"pages\":\"227-237\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"离散数学期刊(英文)\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.4236/OJDM.2016.64019\",\"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.2016.64019","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
G. C. Ying, Y. Y.孟，B. E. Sagan, V. R. Vatter[1]找到了最多包含两个循环的连通图中最大独立集的最大个数。本文给出了n≥12阶连通图中最大独立集的最大数的一个替代证明。我们还描述了达到这个最大值的极值图。
An Alternative Proof of the Largest Number of Maximal Independent Sets in Connected Graphs Having at Most Two Cycles
G. C. Ying, Y. Y. Meng, B. E. Sagan, and V. R. Vatter [1] found the maximum number of maximal independent sets in connected graphs which contain at most two cycles. In this paper, we give an alternative proof to determine the largest number of maximal independent sets among all connected graphs of order n ≥ 12, which contain at most two cycles. We also characterize the extremal graph achieving this maximum value.
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