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Representation of smooth surfaces by graphs. Transformations of graphs which do not change the Euler characteristic of graphs

✍ Scribed by Alexander V. Ivashchenko

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 817 KB
Volume: 122
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90297-7

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✦ Synopsis

A molecular space is a family of closed unit cubes in Euclidean space E". 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", spheres s", a torus and a projective plane in molecular space and graph representations.

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In this paper we continue to study properties of contractible transformations of graphs. We prove that contractible transformations do not change the homology groups of graphs.