应用联树模型,把图浸入平面,获得这个图的关联曲面,从而获得这个图的嵌入曲面的亏格。应用这个方法,我们证明了2个著名的亏格等式。第1如果e是图G的一条割边,G-e有2个分支G1,G2,那么,g(G1)+g(G2)=g(G)。其中g(G)表示图G的亏格。第2用H*υK表示图Ⅳ与K在点υ处的结合,即V(H)∩V(K)=υ,E(H)∩ E(K)=φ.γ(G)表示图G的最小可定向亏格。那么,γ(H*υK)=γ(H)+γ(K)。
In the paper, we employ the joint tree model to immerse a graph on the plane, and obtain an associate surface of the graph. Therefore, we obtain the genus of an embedding surface of the graph. By the way,we prove two genus identities of graphs which are well-known in literature. Firstly,if e is a cut edge of G, G1, G2 are two components of G - e, then, g(G1) + g(G2) = g(G), where g(G) represents a genus of G. Secondly, let H * υK denote the amalgamation of a graph H and K at the point v, i. e.V(H)∩V(K)=υ,E(H)∩ E(K)=φ.γ(G)represent the minimum genus of G.then,γ(H*υK)=γ(H)+γ(K).