More characterizations of triangulated graphs

New characterizations of triangulated and cotriangulated graphs are presented. Cotriangulated graphs form a natural subclass of the class of strongly perfect graphs, and they are also characterized in terms of the shellability of some associated collection of sets. Finally, the notion of stability function of a graph is introduced, and it is proved that a graph is triangulated if and only if the polynomial representing its stability function has all its coefficients equal to 0, +1 or −1.