论文标题
二进制不同中央部分的猜想
A conjecture on different central parts of binary trees
论文作者
论文摘要
让$ω_n$是通过识别带有二进制二进制二进制二进制的rgood二进制树的根来获得的$ n $顶点的二进制树的家族。史密斯等人在题为“树的不同中部的不同中部（电子杂志），第3号，第3期，纸3.17，32 pp）中。推测在所有$ n $顶点的所有二进制树中，中心的任何两个中心之间的成对距离，质心和子树核心受到家庭的某些成员$ω_n$的最大化。我们首先获得了根系的二进制树，该树将包含子树的根数量最小化，然后证明此猜想。我们还获得了最大化这些距离的二进制树。
Let $Ω_n$ be the family of binary trees on $n$ vertices obtained by identifying the root of an rgood binary tree with a vertex of maximum eccentricity of a binary caterpillar. In the paper titled "On different middle parts of a tree (The electronic journal of combinatorics, 25 (2018), no. 3, paper 3.17, 32 pp)", Smith et al. conjectured that among all binary trees on $n$ vertices the pairwise distance between any two of center, centroid and subtree core is maximized by some member of the family $Ω_n$. We first obtain the rooted binary tree which minimizes the number of root containing subtrees and then prove this conjecture. We also obtain the binary trees which maximize these distances.
