紧图是现代图论的一个重要分支，是对Birkho?定理的一种推广。本文主 要讨论了一些关于紧图的构造方法，在已有的紧图研究基础上扩充紧图类。 本文主要包含以下三部分内容。 第一部分介绍了本文的研究背景，预备知识及主要研究成果。 第二部分考虑完全图加边后的紧性，证明了无孤立点的n阶紧图加n个悬 挂点构成的图G仍为紧图。n阶完全图加k个悬挂点构成的图为紧图。在此基 础上，证明完全图的k个点连接2阶链为紧图。进一步拓展，发现可以证明全 完图的k个点连接3阶链为紧图。由此将证明推广到将n阶完全图的点与k条s阶 链对应相连构成的图仍为紧图。 第三部分探究以圈为基础构造紧图。首先证明了圈上的每个点均加k条悬 挂点构造出的图仍为紧图。其次又发现在(3,2)星圈上加悬挂点构成的图G为 紧图。进一步证明圈上的每个点均与 k条2阶链相连，组成的图仍为紧图。

Compact graph is an important branch of modern graph theory, which can be considered as a generalization of the famous Birkho? theorem. In this paper, Some new methods are applied to construct compact graph under the former results. This paper consists of three sections. In the ?rst section, the background knowledge, the necessary prerequisites and brief description of the main results of this paper are shown. In the second part, the compact graphs are obtained by adding pendant edges of complete graph. The proof of the compactness of the graph of n-order complete graph with k pendant edges proves that the 2nd-order chain connected by k vertices of a complete graph is compact. Further analysis shows that k vertices of complete graphsareconnectedtothethird-orderchainofcompactgraphs. Thus,wecanprove that the graphs composed of the vertices of n-order complete graphs and k s-order chains are still compact graphs. Inthethirdpart,weconstructcompactgraphsbasedoncycles. Firstly,weprove that graphs constructed by adding k pendant edges to every vertices on a cycle are still compact graphs. Then it is proved that a graph consisting of every vertices on a circle connected with k chains of order 2 is still compact.