{"title":"超prism 的生成树数量","authors":"Z. R. Bogdanowicz","doi":"10.47443/dml.2024.004","DOIUrl":null,"url":null,"abstract":"Let the vertices of two disjoint and equal length cycles be denoted u 0 , u 1 , . . . , u n − 1 in the first cycle and v 0 , v 1 , . . . , v n − 1 in the second cycle for n ≥ 4 . The superprism ˘ P n is defined as the graph obtained by adding to these disjoint cycles all edges of the form u i v i and u i v i +2 (mod n ) . In this paper, it is proved that the number of spanning trees in ˘ P n is n · 2 3 n − 2 .","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The number of spanning trees in a superprism\",\"authors\":\"Z. R. Bogdanowicz\",\"doi\":\"10.47443/dml.2024.004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let the vertices of two disjoint and equal length cycles be denoted u 0 , u 1 , . . . , u n − 1 in the first cycle and v 0 , v 1 , . . . , v n − 1 in the second cycle for n ≥ 4 . The superprism ˘ P n is defined as the graph obtained by adding to these disjoint cycles all edges of the form u i v i and u i v i +2 (mod n ) . In this paper, it is proved that the number of spanning trees in ˘ P n is n · 2 3 n − 2 .\",\"PeriodicalId\":36023,\"journal\":{\"name\":\"Discrete Mathematics Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-04-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.47443/dml.2024.004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/dml.2024.004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
设两个不相交且长度相等的循环的顶点分别记为第一个循环中的 u 0 , u 1 , ., 第一个循环中的 u n - 1 和第二个循环中的 v 0 , v 1 , ., v n - 1 在 n ≥ 4 的第二个周期中。超prism ˘ P n 被定义为在这些互不相交的循环中加入所有形式为 u i v i 和 u i v i +2 (mod n ) 的边所得到的图形。本文证明，˘ P n 中的生成树数为 n - 2 3 n - 2 。
Let the vertices of two disjoint and equal length cycles be denoted u 0 , u 1 , . . . , u n − 1 in the first cycle and v 0 , v 1 , . . . , v n − 1 in the second cycle for n ≥ 4 . The superprism ˘ P n is defined as the graph obtained by adding to these disjoint cycles all edges of the form u i v i and u i v i +2 (mod n ) . In this paper, it is proved that the number of spanning trees in ˘ P n is n · 2 3 n − 2 .
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