For an edge-colored graph G, a set F of edges of G is called a proper edge-cut if F is an edge-cut of G and any pair of adjacent edges in F are assigned different colors. An edge-colored graph is proper disconnected if for each pair of distinct vertices of G there exists a proper edge-cut separating them. For a connected graph G, the proper disconnection number of G, denoted by pd(G), is the minimum number of colors that are needed in order to make G proper disconnected. In this paper, we first give the exact values of the proper disconnection numbers for some special families of graphs. Next, we obtain a sharp upper bound of pd(G) for a connected graph G of order n, i.e, \(pd(G)\le \min \{ \chi '(G)-1, \left\lceil \frac{n}{2} \right\rceil \}\). Finally, we show that for given integers k and n, the minimum size of a connected graph G of order n with \(pd(G)=k\) is \(n-1\) for \(k=1\) and \(n+2k-4\) for \(2\le k\le \lceil \frac{n}{2}\rceil \).

对于边缘着色图G，如果F是G的边缘切割，并且F中的任何一对相邻边缘被分配了不同的颜色，则G的一组边缘F被称为适当的边缘切割。如果对于G的每对不同的顶点都存在将它们分开的适当的切边，则边缘着色的图正确断开。对于连通图G，用pd（G）表示的G的正确断开数是使G所需的最小颜色数正确断开连接。在本文中，我们首先给出一些特殊族图的正确断开数的确切值。接下来，对于阶数为n的连通图G，我们获得pd（G）的尖锐上限，即\（pd（G）\ le \ min \ {\ chi'（G）-1，\ left \ lceil \ frac {n} {2} \ right \ rceil \} \）。最后，我们表明对于给定的整数k和n，对于\（k = 1 \），具有\（pd（G）= k \）的n阶连通图G的最小大小为\（n-1 \）。和\（N + 2K-4 \）为\（2 \ le k \ le \ lceil \ frac {n} {2} \ rceil \）。