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For a graph $G$ with the vertex set $V(G)$ and the edge set $E(G)$ and a starsubgraph $S$ of $G$, let $\alpha_S(G)$ be the maximum number of vertices in $G$such that no two of them are in the same star subgraph $S$ and $\theta_S(G)$ bethe minimum number of star subgraph $S$ that cover the vertices of $G$. A graph$G$ is called $S$-perfect if for every induced subgraph $H$ of $G$,$\alpha_S(H)=\theta_S(H)$. Motivated by perfect graphs discovered by Berge,Ravindra introduced $S$-perfect graphs. In this paper we prove that atriangulated graph is $S$-perfect if and only if $G$ is odd sun-free. Thisresult leads to a conjecture which if proved is a structural characterizationof $S$-perfect graphs in terms of forbidden subgraphs.

Odd sun-free Triangulated Graphs are $S$-perfect