关于无三角形图和无$C_4$图中邻近度等距离参数的区别
On the difference between proximity and other distance parameters in triangle-free graphs and $C_4$-free graphs
摘要：
连通图$G$的顶点$v$的平均距离是从$v$到$G$的所有其他顶点的距离的算术平均值。$G$的邻近度$π(G)$和远离度$ρ(G)$是$G$的顶点的平均距离的最小值和最大值。本文给出了具有给定阶和最小度的无三角形图的距离与邻近、直径与邻近、半径与邻近之差的上界。我们得到后两个结果，首先证明下界的顺序，最小程度和直径或半径方面的接近。我们的边界是尖锐的除了一个加法常数。我们还得到了相应的界限$C_4$ -自由图。
英文摘要：
The average distance of a vertex $v$ of a connected graph $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The proximity $π(G)$ and the remoteness $ρ(G)$ of $G$ are the minimum and the maximum of the average distances of the vertices of $G$. In this paper, we give upper bounds on the difference between the remoteness and proximity, the diameter and proximity, and the radius and proximity of a triangle-free graph with given order and minimum degree. We derive the latter two results by first proving lower bounds on the proximity in terms of order, minimum degree and either diameter or radius. Our bounds are sharp apart from an additive constant. We also obtain corresponding bounds for $C_4$-free graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
