New methods for reducing size graphs

Size theory is an method used approach for the problem of comparing the shapes of topological spaces, based on mathematical transform called size function. In computing discrete size functions, the components of particular subgraphs of a graph labelled at its vertices, called size graph, need to be counted. The smaller the graph, the faster the computation. Two method of reducing size graphs without changing the corresponding discrete size functions, that is ℓ-reduction and Δ-reduction, are presented. The main properties of these two methods are studied and some useful theorems about them are proved.