中文摘要：

令Γ是S^3中的一个抽象平面图，Γ’是在图Γ上加上有限条边后所得到的图．主要考虑图Γ’的抽象平面性，并且给出了Γ’是抽象平面图的一个充要条件，另外还从平坦嵌入的角度对平面图做了一些讨

英文摘要：

Let Γ be an abstractly planar graph in S^3 , and Γ＇ a graph obtained by adding a finite number of edges to Γ. The abstract planarity of Γ＇ is considered. A necessary and sufficient condition under which Γ＇ is abstractly planar is given. Some discussions of planar graph in the viewpoint of flat embedding are done.