青年科学基金项目取得了如下进展：出版专著（Springer出版社）1部、译著1部，（接受）发表科研论文13篇（其中11篇为SCI检索杂志），已发表11篇，接受发表2篇；用概率方法将Krivelevich等人的结果改进到几乎最好；建立了图能量（度的幂和的一种推广）比较的新方法，彻底解决了多个长期未决的公开问题和猜想。近年来，度的幂和的极值问题得到了包括Erdos、Bollobas和Katona等国际知名学者的关注和重视。最近Bollobas等人提出了与度的幂和相关的两类Turan问题并进行了深入研究。本项目将在青年科学基金项目的基础上，围绕Bollobas等人提出的一系列公开问题，继续研究度的幂和的极值问题，特别是两类Turan问题。我们将参考现有的研究方法，将经典图论方法与概率方法相结合，用图变换与分析结合的方法来开展研究，争取发展出一套系统的研究方法，这无疑将是对极图理论的新贡献。

Supported by NSFC, the project has made many progress. We list as follows: One monograph (Springer), one translation and 11 papers are published and 2 papers are accepted for publication. The results of Krivelevich and Yuster are improved to be almost best by using the probabilistic method; One new method to compare the values of graph energy is established, from which some long-time unsolved open problems and conjectures are completely solved. In these years, the extremal problems on the sum of degree powers are very popular. Recently, Bollobas et al. investigated two new classes of Turan problems concerning the sum of degree powers of graphs. In this project, we will continue to consider the extremal problems on the sum of degree powers of graphs, especially the two new classes of Turan problems, and investigate a list of open problems proposed by Bollobas et al.. The main method we will use are the classical methods, the probabilistic method, graph transforms, analysis method, and so on. We are willing to obtain some new results and expand some systemic methods, which will be a new contribution to extramal graph theory.