图的生成树,基本圈与Betti亏数

Spanning Trees, Basic Cycles and Betti Deficiency of a Graph

G为图且T是G的一棵生成树.记号ξ(G,T)表示G＼E(T)中边数为奇数的连通分支个数.文献[2]称ξ(G)=minξ(G,T)为图G的Betti亏数,这里min取遍G的所有生成树T.由文献[2]知,确定一个图G的最大亏格主要确定这个图的Betii亏数ξ(G).该文研究与Betti亏数有关的图的特征结构,得到了关于图的最大亏格的若干结果.

Let G be a graph and T be a spanning tree of it. The sign ξ(G, T) denotes the number of components of G\E(T) with odd number of edges, and it is known that the value ξ(G) = minξ(G, T) is defined as Betti deficiency of G , where min is taken over allspanning trees of G . In this paper the authors study the characteristic structure of a graph connecting to its Betti deficiency, and obtain some new results on the maximum genus of a graph.