Ebook: Topological Theory of Graphs

This book introduces polyhedra as a tool for graph theory and discusses their properties and applications in solving the Gauss crossing problem. The discussion is extended to embeddings on manifolds, particularly to surfaces of genus zero and non-zero via the joint tree model, along with solution algorithms. Given its rigorous approach, this book would be of interest to researchers in graph theory and discrete mathematics.

• Establishes a self-contained theoretical framework for graph theory from a topological point of view.
• Explains the embedding of graphs on non-zero genus surfaces.
• Discusses graphic matroids and knot polynomials.