{"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":1,"journal":{"name":"Accounts of Chemical Research","volume":"28 3","pages":""},"PeriodicalIF":17.7000,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/dml.2024.004","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
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 .
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 。
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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