On $\omega \psi$-Perfect Graphs

In this paper, we generalize the concept of {\it{perfect graphs}} to other parameters related to graph vertex coloring. This idea was introduced by Christen and Selkow in 1979 and Yegnanarayanan in 2001. Let $a,b \in \{ \omega, \chi, \Gamma, \alpha, \psi \}$ where $\omega$ is the clique number, $\chi$ is the chromatic number, $\Gamma$ is the Grundy number, $\alpha$ is the achromatic number and $\psi$ is the pseudoachromatic number. A graph $G$ is \emph{$ab$-perfect}, if for every induced subgraph $H$ of $G$, $a(H)$ equals $b(H)$. In this paper, we characterize the $ab$-perfect graphs when $a=\omega$ and $b=\psi$.