论文标题
关于树木的极端叶子状态和内部状态
On extremal leaf status and internal status of trees
论文作者
论文摘要
对于一棵树$ t $的顶点$ u $，$ u $的叶子（分别为内部）状态是$ u $到所有叶子（分别是内部顶点）$ t $的距离的总和。树$ t $的最小（最大）叶状态是$ t $的所有顶点的最小（最大）叶状态。树$ t $的最小内部状态（分别为最大）是$ t $的所有顶点的最小（最大）内部状态。我们给出了最小叶状态，最大叶子状态，最小内部状态以及树的最大内部状态的最小和最大值，并表征了极端情况。我们还讨论了具有给定直径或最高程度的树的这些参数。
For a vertex $u$ of a tree $T$, the leaf (internal, respectively) status of $u$ is the sum of the distances from $u$ to all leaves (internal vertices, respectively) of $T$. The minimum (maximum, respectively) leaf status of a tree $T$ is the minimum (maximum, respectively) leaf statuses of all vertices of $T$. The minimum (maximum, respectively) internal status of a tree $T$ is the minimum (maximum, respectively) internal statuses of all vertices of $T$. We give the smallest and largest values for the minimum leaf status, maximum leaf status, minimum internal status, and maximum internal status of a tree and characterize the extremal cases. We also discuss these parameters of a tree with given diameter or maximum degree.
