# 华南师范大学尤利华教授；华中师范大学李书超教授 学术报告

A {\em star set} for $\mu$ in $G$ is a subset $X$ of $V(G)$ such that $\left | X \right |=k$ and $\mu$ is not an eigenvalue of $G-X$, where $G-X$ is the subgraph of $G$ induced by $\overline{X}=V(G)\setminus X$. In this situation $H=G-X$ is called a {\em star complement} for $\mu$.

In this talk, we introduce the study on the star sets and star complements:

(1) characterize the regular graphs with a given graph as a star complement for an eigenvalue  $\mu$;

(2) characterize the maximal graphs with a given graph as a star complement for an eigenvalue  $\mu$.