Total embedding distributions of Ringel ladders

TL;DR

This paper derives an explicit formula for the non-orientable embedding distributions of Ringel ladders, expanding the understanding of their topological properties beyond previously known orientable cases.

Contribution

It provides the first explicit formula for non-orientable embeddings of Ringel ladders, complementing existing results on their genus distribution.

Findings

Explicit formula for non-orientable embeddings of Ringel ladders

Enhanced understanding of total embedding distributions

Extension of topological graph theory results

Abstract

The total embedding distributions of a graph is consisted of the orientable embeddings and non- orientable embeddings and have been know for few classes of graphs. The genus distribution of Ringel ladders is determined in [Discrete Mathematics 216 (2000) 235-252] by E.H. Tesar. In this paper, the explicit formula for non-orientable embeddings of Ringel ladders is obtained.