Domination Number and Hamiltonicity of Graphs

Abstract

Let $G$ be a $k$-connected ($k\ge 2$) graph of order $n$. If $\gamma (G^c)\ge n–k$, then $G$ is Hamiltonian or $K_k\vee K_{k+1}^c$, where $\gamma (G^c)$ is the domination number of the complement of the graph $G$.