REPRESENTATION OF SMOOTH SURFACES BY GRAPHS - TRANSFORMATIONS OF GRAPHS WHICH DO NOT CHANGE THE EULER CHARACTERISTIC OF GRAPHS

A molecular space is a family of closed unit cubes in Euclidean space E(n). Cube vertices have integer coordinates. Molecular spaces can be transformed from one to the other by four kinds of contractible transformations. In this paper we apply contractible transformations of molecular spaces to graphs. We prove that these transformations do not change the Euler characteristic of a graph. We describe some continuous spaces: the plane space E(n), spheres S(n), a torus and a projective plane in molecular space and graph representations.