一类极大临界h连通图的性质

Nature of A kind of Maximal Critically h-Connected Graphs

设G是h连通图 ,图G的顶点v称为临界点 ,G-v不再h连通 ,如果G的每一个顶点都是临界的 ,则称G为临界h连通图 .对于G中任意两个不相邻的顶点x与y ,G +xy不再临界h连通 ,则称G为极大临界h连通图 .引入图的粘合的概念 ,讨论了δ(G) =3h/ 2 - 1的极大临界h连通图的性质 ,得到了这类图有关原子 ,最小点割和分支的重要性质 ,这有利于进一步研究这类图的结构 .

Let h be an integer with h≥2.A graph G is called critically h-lonnected if G is h connected but,for every vertex v of G, G-v is not h-connected. A critically h-connected graph G is maximal if G+uv is not critically h-connected for any pair of nonadjacent vertices u and v of G.In terms of the critically h-connected graphs and the maximal h-connected graphs of δ(G)=3h/2-1,some natures have been clarified in Bibliograph 3 and Bibliograph 4. In the article, the conception of graphical pasting is introduced based on them, the nature of the maximal critically h-connected graphs of δ(G)=3h/2-1 is discussed,some natures about the atom, mimimum cutsets and components is found, it helps to do the further research on the structure of such graphs.