Lower bound on the number of the maximum genus embedding of $K_{n,n}$

TL;DR

This paper introduces a method to establish a lower bound on the number of maximum genus embeddings of complete bipartite graphs, specifically for odd n, improving previous results by Stahl and Ren.

Contribution

The paper presents a novel method to determine lower bounds on the number of maximum genus embeddings of K_{n,n} for odd n, advancing prior research.

Findings

Provides a new lower bound for maximum genus embeddings of K_{n,n}

Improves upon previous results by Stahl and Ren

Applicable to complete bipartite graphs with odd n

Abstract

In this paper, we provide an method to obtain the lower bound on the number of the distinct maximum genus embedding of the complete bipartite graph Kn;n (n be an odd number), which, in some sense, improves the results of S. Stahl and H. Ren.