图中的接近度、距离和最大度

P. Dankelmann, Sonwabile Mafunda, Sufiyan Mallu
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引用次数: 1

摘要

连通图$G$的顶点$v$的平均距离是$v$到$G$所有其他顶点距离的算术平均值。$G$的接近度$\pi(G)$和距离$\rho(G)$分别是$G$的顶点平均距离的最小值和最大值。本文给出了给定阶数、最小度和最大度的图的距离和接近的上界。我们的界限是由一个附加常数得到的。
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Proximity, remoteness and maximum degree in graphs
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 $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the maximum of the average distances of the vertices of $G$, respectively. In this paper, we give upper bounds on the remoteness and proximity for graphs of given order, minimum degree and maximum degree. Our bounds are sharp apart from an additive constant.
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