讲座内容：

We study the maximum of the degree powers sum $e_p(G) = \sum_{v \in V(G)} d(v)^p$ in two settings. First, for sufficiently large bowtie-free graphs $G$ of order $n$, we asymptotically determine $ex_p(n, F_2)$ and characterize the extremal structure: it essentially consists of a complete bipartite graph with a single edge added inside the smaller part. Second, among all unicyclic graphs of order $n$ and diameter $d \ge 1$, we prove that the maximum of $e_p(G)$ for $p \ge 2$ is uniquely attained by an explicit family $H^d$. These results extend the Turán-type problem of degree powers sum to both forbidden subgraph and diameter-constrained contexts.