On enumeration of a class of toroidal graphs

Abstract

We present enumerations of a class of toroidal graphs which give rise to semi-equivelar maps. There are eleven different types of semi-equivelar maps on the torus. These are of the types $\{3^6\}$, $\{4^4\}$, $\{6^3\}$, $\{3^3,4^2\}$, $\{3^2,4,3,4\}$, $\{3,6,3,6\}$, $\{3^4,6\}$, $\{4,8^2\}$, $\{3,12^2\}$, $\{4,6,12\}$, $\{3,4,6,4\}$. We know the classification of the maps of types $\{3^6\}$, $\{4^4\}$, $\{6^3\}$ on the torus. In this article, we attempt to classify maps of types $\{3^3,4^2\}$, $\{3^2,4,3,4\}$, $\{3,6,3,6\}$, $\{3^4,6\}$, $\{4,8^2\}$, $\{3,12^2\}$, $\{4,6,12\}$, $\{3,4,6,4\}$ on the torus.

Cited by in corpus (1)

• On enumeration of a class of maps on Klein bottle