A characterization of chordal graph without sun and co-rising sun as convex geometry

In this paper we introduce the notion of $t_3$ \textit{convexity}, a natural restriction of triangle convexity. A \textit{triangle path} is a path allowing just short chords. A triangle path $P$ between two non-adjacent vertices in a graph $G$ is called $t_3$ \textit{path} if the first vertex of $P$ is among vertices from $P$ adjacent only to the second vertex of $P$, and the last vertex of $P$ is among vertices from $P$ adjacent only to the second-last vertex of $P$. A set $S \subseteq V(G)$ is