The Number Of Maximum Genus Embeddings (MGE's) Of Graphs

Topological graph theory is the main branch of graph theory it deals graphs as topological spaces,their embeddings on surf'aces and other associated properties.The chief objectives of topological graph theory are to study the embeddings of a graph on surfaces.There are many results on the maximum genus,among them,most results are written for the existence of values of such embeddings,and very few graph theorists paid attention to the enumeration of such embeddings and their applications.In this thesis,we review some relevant previous results.Then we provide a method to obtain the lower bound on the number of the distinct maximum orientable genus embeddings of a Halin a graph and a Petersen graph.Our results also work for the lower bound of the number of maximum non-orientable genus embeddings of the given graphs.