论文标题
三角剖分和四边形的接近度
Proximity in Triangulations and Quadrangulations
论文作者
论文摘要
令$ g $为连接的图。如果$ \barσ（v）$表示从$ v $到$ g $的所有其他顶点的算术平均值，则$ g $的$π（g）$，定义为所有Vertices $ v $ v $ g $的最小值。我们为简单的三角剖分和给定的顺序和连通性的四个二动性提供了上限。我们还构建了给定顺序和连通性的简单三角剖分和四边形，它们渐近地匹配上限，并且可能是最佳的。
Let $ G $ be a connected graph. If $\barσ(v)$ denotes the arithmetic mean of the distances from $v$ to all other vertices of $G$, then the proximity, $π(G)$, of $G$ is defined as the smallest value of $\barσ(v)$ over all vertices $v$ of $G$. We give upper bounds for the proximity of simple triangulations and quadrangulations of given order and connectivity. We also construct simple triangulations and quadrangulations of given order and connectivity that match the upper bounds asymptotically and are likely optimal.
