Number of Embeddings of Wheel Graphs on Surfaces of Small Genus

Abstract

In this paper, we obtain the numbers of embeddings of wheel graphs on some orientable and nonorientable surfaces of small genera, mainly on torus, double torus, and nonorientable surfaces of genus $1,2,3$, and $4$. These are the first results for embeddings of wheel graphs on nonorientable surfaces as known up to now.