About the number of vines and regular vines on n nodes
About the number of vines and regular vines on n nodes
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关于n个节点上的藤蔓和常规藤蔓的数量
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
D. Kurowicka
中科院分区：
文献类型：
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作者：
O. M. Nápoles;R. Cooke;D. Kurowicka
图论不仅对组合问题很重要，而且在物理学、电气工程、化学、社会心理学和运筹学研究中也很重要。标记树在概率论中有应用。这些天体在1889年由凯莱首次成功计数。藤蔓使树木长得更长。它们是Cooke在1997年提出的，并已被应用于不确定度分析中。最近在统计学中的应用已经发展，其中根据其图形结构区分葡萄树是重要的[1]，[2]，[3]，[4]，[5]。本文将讨论关于n个结点上标号树个数的已有结果。以前用于描述树的一些想法将被扩展到描述n个节点上的葡萄树。算法来建立葡萄树，连同结果的葡萄树的数量在n个节点上。
The theory of graphs is important not only for combinatorial problems but in physics, electrical engineering, chemistry, social psychology, and research of operations. Labeled trees find application in probability theory. These objects were first successfully counted by Cayley in 1889. Vines generalize trees. They were introduced by Cooke in 1997 and they have been applied in uncertainty analysis. More recently applications in statistics have been developed in which distinguishing vines according to their graphical structure is of importance [1], [2], [3], [4], [5]. In this paper, previous results about the number of labeled trees on n nodes will be discussed. Some of the ideas previously used to characterize trees will be extended to characterize vines on n nodes. Algorithms to build vines, together with a result about the number of vines on n nodes will be presented.