A 3 - restricted edge cut is such an edge cut that separates a connected graph into a disconnected one with each component having order at least 3 摘要3限制性边割将连通图分离成不连通图，使其各连通分支含有至少3个顶点。
In this paper , we give the necessary and sufficient conditions of the existence of a ( ( kn ( t ) ) , f ) - design for any conneted graph with four vertices 本文中，我们给出了对于任一四点连通图f ，设计存在的必要且充分条件。
We propose some new ideas for finding the graphs , which has minimal or maximal value of the topological index among all the graphs with n vertices and m edges 对n个顶点m条边的简单连通图，哪些图具有最小或最大的拓扑指标值也做了深入的研究。
Given the number of vertices and the number of edges in a class of graphs , the problem of how to determine a graph that has the minimum integrity among the class is studied 对于所有的顶点数和边数都给定的连通图类，如何确定该图类中完整度最小的图。
Among all the graphs with n vertices or m edges and some special graphs , the graphs that have minimal or maximal value of the topological index are found 对于给定顶点数或边数的简单连通图以及在一些特殊图类中，确定了哪些分子图具有最小或最大的拓扑指标值。
( 2 ) for any connected graph g if there is at more one cycle , than and by proofing conclusion 2 , we obtain findings on unique smallest domination set ( 2 )对于连通图g来说，若图g中最多有一个图，那么而在证明结论( 2 )时，本文得出了唯一最小控制集的一个充分条件
Also , if the number of vertices and the integrity in a class of graphs are fixed , the problem of how to determine a graph that has the maximum number of edges among them is investigated 同时研究了对于顶点数和完整度都给定的连通图类，如何确定该图类中边数最多的图的问题。
We derive some properties of gdk ( g ) and show that every fc - regular / c - connected graph on n vertices has generalized fc - diameter at most n / 2 and this upper bound is tight when n = 2k ? 3 + i ( k ? 2 ) 给出gd k ）的一些性质并且证明了n个顶点的k正则k连通图的广义k直径至多为n乃，当n ? 。 zk ? 3淋一2 ）对，该上界是可以达到的
That is to say : r ( x ) = r ( y # dh ( r ( n ( x ) ) , r ( n ( y ) ) ) 1 , on the base of robert and li sheng , i have a deeper research . i define a notion d ( g ) of graph , then carry another research for the graphs with no isolated vertices 给出了一个连通图的直径d ( g )的概念，并且作出连通图总是-域近角色分配的这一结果，其中[ 2 ， d ( g ) ] 。
In this paper , the properties of the maximal critically 4 - connected are iscussed and a new procedure for constructing the maximal critically 4 - connected graph is determined by means of graphical pasting 摘要引入图的粘合的概念，讨论了极大临界4连通图的性质，给出了一个图是这类图的一个充分必要条件，由此给出该类图的一种新的构造方法。
