{"title":"毛毛虫的数量","authors":"Christian Barrientos","doi":"10.19184/ijc.2022.6.2.1","DOIUrl":null,"url":null,"abstract":"<p style=\"text-align: justify;\">A caterpillar is a tree obtained from a path by attaching pendant vertices. The number of caterpillars of size <em>n</em> is a well-known result. In this work extend this result exploring the number of caterpillars of size <em>n</em> together with the cardinalities of the stable sets and the diameter. Three closed formulas are presented, giving the number of caterpillars of size <em>n</em> with: (i) smaller stable set of cardinality <em>k</em>, (ii) diameter <em>d</em>, and (iii) diameter <em>d</em> and smaller stable set of cardinality <em>k</em>.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"30 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the number of caterpillars\",\"authors\":\"Christian Barrientos\",\"doi\":\"10.19184/ijc.2022.6.2.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p style=\\\"text-align: justify;\\\">A caterpillar is a tree obtained from a path by attaching pendant vertices. The number of caterpillars of size <em>n</em> is a well-known result. In this work extend this result exploring the number of caterpillars of size <em>n</em> together with the cardinalities of the stable sets and the diameter. Three closed formulas are presented, giving the number of caterpillars of size <em>n</em> with: (i) smaller stable set of cardinality <em>k</em>, (ii) diameter <em>d</em>, and (iii) diameter <em>d</em> and smaller stable set of cardinality <em>k</em>.</p>\",\"PeriodicalId\":13506,\"journal\":{\"name\":\"Indonesian Journal of Combinatorics\",\"volume\":\"30 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indonesian Journal of Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.19184/ijc.2022.6.2.1\",\"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.2022.6.2.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A caterpillar is a tree obtained from a path by attaching pendant vertices. The number of caterpillars of size n is a well-known result. In this work extend this result exploring the number of caterpillars of size n together with the cardinalities of the stable sets and the diameter. Three closed formulas are presented, giving the number of caterpillars of size n with: (i) smaller stable set of cardinality k, (ii) diameter d, and (iii) diameter d and smaller stable set of cardinality k.
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