Biplab Basak
Published 2016-02-24Version 1
Motivated by the theory of crystallizations, we consider an equivalence relation on the class of $3$-regular colored graphs and proved that up to this equivalence $(a)$ there exists a unique contracted 3-regular colored graph if the number of vertices is $4m$ and $(b)$ there are exactly two such graphs if the number of vertices is $4m+2$ for $m\geq 1$. Using this, we present a simple proof of the classification of closed surfaces.
Comments: 9 pages, 8 figures
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