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In this paper, the maximum graph packing and the minimum graph covering of two graphsD_1, D_2 with six vertices and eight edges and the 8-cycle C_8 are researched.

在统一的构作方法下，对于两个六点八边图所有可能的v和λ给出了相应的最大图填充和最小图覆盖的构造。

Furthermore, two overlapping morph targets may cover a number of vertices that are of relevance for one particular measure.

此外，两个重叠的变形目标可能包括一些顶点是相关的一个具体措施。

If the edges are ordered pairs of vertices then we get the notions of a directed graph and directed multigraph.

如果边都是顶点的有序对，则得到有向图和有向重图的概念。

Like the above result, any two vertices which are of distance 2 is discussed, then we obtain the following result in this thesis: let G be a graph of order n ≥ 3 such that d + d ≥ [(4n)/3] - 1 where d = 2 in G, then every vertex of G is contained in a 3-cycle.

类似上面结论，我们也只考虑图中距离为2的点对，得到下面结论：若对G中的任意距离为2的点u和v有d+d≥[4n/3]-1，那么G中的每个点都含在一个3圈中。

Let α to be independence number of graph G, in 1984 Fan showed: Let G be a 2-connected graph of order n, for every pair vertices x,y of d=2, if max{d,d}≥n/2, then G is Hamiltonian.

1984年，Fan给出了著名的Fan定理：若2连通n阶图G的距离是2的任意两点x、y均有max{d，d}≥n/2，则G是哈密尔顿图。

Ringel's conjecure is that, if T is a tree with n vertices, then graph K_{2n-1} can be partitioned into 2n-1 trees that are isomorphic to T.

标号的研究，是由1963年Ringle提出的一个猜想引出的。

In [29], the author gave that let G be a 2-connected graph with order n and S ≥ t, if |N ∪ N|≥ n - t for any nonadjacent vertices u and v in G, then G is pancyclic or n = 2t, G ≌ K_.

在[29]中，作者给出定理：设G是一个n阶2-连通图，且δ≥t，若对G中的任意两个不相邻的点u和v有|N∪N|≥n-t，那么G是一个泛圈图或n=2t，G≌K_。

In the geometry compression approaches presented in this thesis, the representation of a polygonal mesh is divided into two parts: the first part is termed topology information, which refers to the connectivity of the vertices in the mesh; the second part is termed as geometry information, which refers to the vertex locations and other attributes including color, normal, texture coordinates etc.

在本文中，一个多边形网格的数据表示为两部分：第一部分叫做拓扑信息，指多边形网格顶点之间的连接关系；第二部分叫做几何信息，指多边形网格坐标、颜色、法向以及纹理坐标等几何属性。

In the geometry compression approaches presented in this thesis, the representation of a polygonal mesh is divided into two parts: namely the topology information, which refers to the connectivity of the vertices in the mesh; and the geometry information, which refers to the vertex locations and other attributes including color, normal, texture coordinates etc.

在本文中，一个多边形网格的数据被分割为两部分：第一部分叫做拓扑信息，指多边形网格顶点之间的连接关系；第二部分叫做几何信息，指多边形网格坐标、颜色、法向以及纹理坐标等几何属性。

The original PRT store transfer information in the vertices which leads low resolution models to have less detail than high resolution ones. In this study, the author proposes a method which combines PRT and normal mapping to bring high detail to low resolution models.

PRT相关论文皆以顶点为单位进行计算，这样的条件造成面数少的模型使用PRT的效果受到相当大的限制，因此本论文将PRT结合法向量贴图技术，可使得低面数模型也能具有非常高的细节表现。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。