A Number Of Labelings For A Kind Of Graceful Tree Spaces And Their Relationship

The definition of a kind of graceful tree spaces were given in this paper.We proved graceful properties of the graceful tree spaces.And on the basis of their graceful properties,we prove that the graceful tree spaces admit bipartite odd grace-ful labeling,edge-magic total labeling,(k,d)-graceful labeling,harmonious labeling,even edge-magic total labeling,and both odd and even edge labeling.In addition,this paper defines a kind of special models of graceful tree spaces,and proves the graceful tree space S,which its foundation is star graph,and the vertexes in the foundation T were replaced with bipartite graceful trees Ti,is graceful.Apart from this,this paper explains a way to construct bipartite graceful tree spaces,edge-magic tree spaces and anti-magic tree spaces by graceful tree space.Meanwhile,we prove the relation of these different labels.At last,we give the application of graceful tree space models on golden fish and to bring about fish space graphs.And we propose some guesses about the application of graceful tree space models in network models.