88304am永利集团

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

卢蓉蓉，中南大学博士，导师冯立华教授。主要研究方向是极值图论。目前，已在《Mathematics》期刊上发表论文一篇。