论文标题
根据顺序和最小程度的无三角形和无C_4图的接近性和远程性
Proximity and remoteness in triangle-free and C_4-free graphs in terms of order and minimum degree
论文作者
论文摘要
令$ g $为有限的连接图。 $ g $的顶点$ v $的平均距离是从$ v $到$ g $的所有其他顶点的算术平均值。 $ g $的偏远$ρ（g）$和接近$π（g）$是$ g $的最大值和最小值的最小距离。在本文中，我们在给定顺序和最小程度的无三角形图的偏远图上提出了一个尖锐的上限，以及在接近度上的相应结合，与添加剂常数相距甚远。我们还介绍了$ C_4 $的偏远和接近给定订单和最低学位的上限，我们证明这些图非常可能是最好的。
Let $G$ be a finite, connected graph. The average distance of a vertex $v$ of $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The remoteness $ρ(G)$ and the proximity $π(G)$ of $G$ are the maximum and the minimum of the average distances of the vertices of $G$. In this paper, we present a sharp upper bound on the remoteness of a triangle-free graph of given order and minimum degree, and a corresponding bound on the proximity, which is sharp apart from an additive constant. We also present upper bounds on the remoteness and proximity of $C_4$-free graphs of given order and minimum degree, and we demonstrate that these are close to being best possible.
