On $Z$-monodromies in embedded graphs

TL;DR

This paper characterizes all permutations that can serve as $z$-monodromies of faces in connected simple finite graphs embedded in surfaces with simple duals, advancing understanding of graph embeddings and face permutations.

Contribution

It provides a complete characterization of permutations realized as $z$-monodromies in such embedded graphs, a novel result in topological graph theory.

Findings

Characterization of all $z$-monodromy permutations

Applicable to graphs with simple duals

Enhances understanding of face permutation structures

Abstract

We characterize all permutations which realize as the $z$-monodromies of faces in connected simple finite graphs embedded in surfaces whose duals are also simple.