부산대학교 도서관

Summary: ``Let $G$ be a connected graph of order $n$, and let $NC2(G)$ denote $\min\{|N(u)\cup N(v)|\:\ {\rm dist}(u,v)=2\}$, where ${\rm dist}(u,v)$ is the distance between $u$ and $v$ in $G$. A cycle $C$ in $G$ is called a dominating cycle if $V(G)\sbs V(C)$ is an independent set in $G$. In this paper, we prove that if $G$ contains a dominating cycle and $\delta\ge2$, then $G$ contains a dominating cycle of length at least $\min\{n,2NC2(G)-3\}$.''