论文标题
给定程度序列或段序列的极端树相对于施泰纳的3个年份
Extremal trees of given degree sequence or segment sequence with respect to Steiner 3-eccentricity
论文作者
论文摘要
图形$ g $的顶点的Steiner $ k $ centricity是所有包含顶点的$ k $ -subsets的最大steiner距离。 ％给出了Steiner 3分子的某些一般特性。令$ \ mathbb {t} _n $为所有$ n $ -vertex树的集合，$ \ mathbb {t} _ {n，δ} $是$ n $ -vertex树的集合，给定最大程度等于$ $ $ $ $ $ $Δ$，$ \ mathb { $ \ mathbb {t} _ {n，δ}^k $是$ n $ vertex树的集合，其恰好$ k $的最大程度等于$δ。$在本文中，我们首先确定$ n $ n $ -n $ vertex树的普通steiner 3-含量为$ n $ vertex的敏锐上限。表征相应的极端图。因此，与大化理论一起，$ \ mathbb {t} _n $之间的唯一图（分别$ \ m athbb {t} _ {n，δ} $，$ \ mathbb {t} _n^k，\ n^k，\ mathbb {t} _ {t} _ {n，δ} _} _ {然后，我们表征了独特的$ n $ vertex树，其给定段序列具有最大的平均史坦纳（Steiner）3年级。同样，确定具有给定数量的段数的$ n $ vertex树，具有最大的平均史坦纳3年级。
The Steiner $k$-eccentricity of a vertex in graph $G$ is the maximum Steiner distance over all $k$-subsets containing the vertex. %Some general properties of the Steiner 3-eccentricity of trees are given. Let $\mathbb{T}_n$ be the set of all $n$-vertex trees, $\mathbb{T}_{n,Δ}$ be the set of $n$-vertex trees with given maximum degree equal to $Δ$, $\mathbb{T}_n^k$ be the set of $n$-vertex trees with exactly $k$ vertices of maximum degree, and let $\mathbb{T}_{n,Δ}^k$ be the set of $n$-vertex trees with exactly $k$ vertices of given maximum degree equal to $Δ.$ In this paper, we first determine the sharp upper bound on the average Steiner 3-eccentricity of $n$-vertex trees with given degree sequence. The corresponding extremal graph is characterized. Consequently, together with majorization theory, the unique graph among $\mathbb{T}_n$ (resp. $\mathbb{T}_{n,Δ}$, $\mathbb{T}_n^k, \mathbb{T}_{n,Δ}^k$) having the maximum average Steiner 3-eccentricity is identified. Then we characterize the unique $n$-vertex tree with given segment sequence having the largest average Steiner 3-eccentricity. Similarly, the $n$-vertex tree with given number of segments having the largest average Steiner 3-eccentricity is determined.
