3-regular colored graphs and classification of surfaces (Q2408210)

In this paper, the author studies 3-regular colored graphs and define an equivalence relation on them. He proves that up to this defined relation, (a) there exists a unique contracted 3-regular colored graph if the number of the vertices is \(4m\) and (b) there are exactly two such graphs if the number of vertices is \(4m+2\) for each \(m>0\). By means of this, he gives a proof of the closed surfaces. The main method used in the proofs is a simple cut and glue operation. The paper is written in a nice way and may be useful in a large area.