Supereulerian Graphs In Generalized Prisms

The supereulerian graph problem is a classic problem in graph theory,and the supereu-lerian property in the real life is also very extensive application.A graph is a supereulerian graph,meaning that it contains a spanning euler subgraph.Generalized prism is also an im-portant research area in recent years.In this paper,based on the concept of generalized prism in graph theory and many research results,as a generalization,the concept of generalized prism of two digraphs is proposed,and the supereulerianity of such graphs are discussed,and the supereulerian correlation properties of generalized prism and the supereulerian properties of undirected generalized prism are studied.This thesis consists of three chapters.In Chapter 1,we present the research backgrounds contents,and some terminologies and notations,and Catlin's Reduction method.In Chapter 2,we give a lemma for judging that a generalized prism is a supereulerian digraph.The lemma proves that the generalized prism is a supereulerian digraph when the number of rotation is r=3.Then some sufficient conditions for the generalized prism to be a supereulerian digraph are given when the number of rotation is r=4,r=5.Finally,we study the supereulerian properties of undirected generalized prisms.In Chapter 3,we introduce the concepts of D-supereulerian graph proposed by Liu et al.then we mainly study the supereulerian properties of G for the ?-generalized prism?H(G)of H when G is a D-supereulerian graph and H is a supereulerian graph.