Book Presentation Of Spatial Graph

The embedding problem of finite graph into three-dimensional Euclidean space R³ is considered as an application and branch of knot theory. We define some special embedding by applying knowledge from knot theory to spatial graph theory in order to observe the properties of spatial graph.Book presentation is a special kind of embedding of spatial graphs with good properties such as locally unknotted. In this paper we discuss some properties of book presentation of spatial graphs and prove that the book presentation of complete graph K_2m is unique up to sheet translation and ambient isotopy. We have the same result with K₇.Research in this field is of great importance to investigating and distinguishing spatial graphs both theoretically and practically.