An edge-colored connected graph $G$ is properly connected if between every pair of distinct vertices, there exists a path such that no two adjacent edges have the same color. Fujita (2019) introduced the optimal proper connection number pc_opt(G) for a monochromatic connected graph $G$, to make a connected graph properly connected efficiently. More precisely, pc_opt ($G$) is the smallest integer $p+q$ when one converts a given monochromatic graph $G$ into a properly connected graph by recoloring $p$ edges with $q$ colors. In this paper, we show that pc_opt ($G$) has an upper bound in terms of the independence number $\alpha \left(G\right)$. Namely, we prove that for a connected graph $G$, pc_opt ($G$)$\le \frac{5\alpha \left(G\right)-1}{2}$. Moreover, for the case $\alpha \left(G\right)\le 3$, we improve the upper bound to 4, which is tight.

边色连通图 $G$如果在每对不同的顶点之间，存在一条路径，使得没有两条相邻的边具有相同的颜色，则正确连接。Fujita (2019) 介绍了单色连通图的最佳适当连接数pc _opt (G)$G$，使连通图有效地正确连接。更准确地说，pc _opt ($G$) 是最小的整数 $磷+q$ 当转换给定的单色图时 $G$ 通过重新着色成正确连接的图形 $磷$ 边与 $q$颜色。在本文中，我们展示了 pc _opt ($G$) 在独立数方面有一个上限 $\alpha \left(G\right)$. 即，我们证明对于连通图$G$, 电脑_选择 ($G$)$\le \frac{5\alpha \left(G\right)-1}{2}$. 此外，对于这种情况$\alpha \left(G\right)\le 3$，我们将上限提高到 4，这是紧的。