  There are many approaches to the classification of Morse functions and their
gradient fields (Morse Fields) on 2-surfaces. This paper studies the gluings of
quadrilaterals and the classification of topological surfaces obtained by
gluing together sides of quadrilateral graphs created by trajectories on
gradient fields with focal critical points as vertices and a saddle point in
center for classification saddle and focus critical points. We review the
graphs embedded into surfaces associated with gluings, the number of possible
gluings, and some algorithms based on labeling schemes of fundamental polygons
that can be used to compute those numbers.
