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  k-graph
We show how our results extend to the case of higher rank graphs, where an analogous result is obtained for the tensor algebra of a row-finite k-graph with no sources.
      
We present some new results on the number of vertices of an (n,k)-graph, depending on new estimations of the transversal number of a uniform hypergraph with a large independent edge set.
      
A finite, simple, undirected graph is called k-critically n-connected, or, briefly, an (n,k)-graph, if it is noncomplete and n-connected and the removal of any set X of at most k vertices results in a graph which is not (n-|X|+1)-connected.
      
We prove that a graph is the graph of a minimally rigid (with respect to edges) (k - 1,k)-frame if and only if it is a (k - 1,k)-graph.
      
A (k - 1,k)-graph is a multi-graph satisfyinge' ≤ (k - 1)v' - k for every non-empty subset ofe' edges onv' vertices, with equality whene' = |E(G)|.
      
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A (p·Δ·k) -graph is a p-point simple graph with maximum degree Δ and connectivity ko In this paper, the maximum number of edges of a (p·Δ·k) -graph is determined.

本文给出了给定阶数,最大度和连通度的简单图的最大棱数。

Let G be a simple undirected graph and C be the complement of C. Call G a (p, p-k) graph if |E(G)|=|V(G)|-K, where V(G), E(G) denote the sets of the vertices and edges of G respectively. Suppose {G1,G2}be a piar of graphs with same order, we call {G1, G2} packable if G1 is isomorthism to a subgraph of G2. P. J. Slater proposed the problem in 1985: "Is it true that trianglefree pairs of (Pm p-1) graphs p≥6, can always be packed?"In this paper we solved the problem.

设G是一个简单无向图,酉麦示G的补图。称G是(p,p-k)图.如果|E(G)|=|V(G)|-K,这里V(G)、E(G)分别表示G的顶点集和边集,又设{G_1,G_2}为同阶图对,若G_1同构于瓦的某个子图,则称图对{G_1,G_2}是可包装的.1985年P. J. Slater曾提出问题:“对于任意两个同阶图(阶数≥6)且不含K_3的(p,p-1)图对是否都可包装”,本文解决了这一问题.

(n、K)-graph is the very important type of n-connected graphs. This paper has obtained some results of (n、K)-graph by using theconcept of Atomic alignment.

(n、K)—图是n—连通图中一类很重要的图。本文利用Atomic序列的概念,得到了关于(n、K)—图的几个结果。

 
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