A Particular Space Side Of The Diagram Homotopy

K4edge homotopy classification is given by Ryo Nikkuni withα-invariant in 2004,and it is pointed out that K4 complete graph,Δ-homotopy, delta vertex-homotopy and edge homotopy are equivalent. Based on this result five vertex complete graph K5 edge homotopy classification was studied by Juan-juan Chen.and it is proved that arbitrary two edges of space embedding K5 is homotopic if and only if it have same number ofα-invarian.In this paper we discuss some special space for the Edge-homotopy problem that when the space vertex degree is not the only, the space is equivalent to the nature of topological map.Special examples graph G,G is given and construct edge-homotopy invariant,prove that the two space map edge of space embedding is homotopic in the case of each vertex degree is not the same, and Preliminary assessment that there is an infinite number of edge space maps homotopic embedding space.Further, for such space plans and other cases also had a preliminary study, and accordingly the nature of such space diagram summarized the characteristics and development of the extension.