The decompositions of line graphs, middle graphs and total graphs of complete graphs into forests

In this paper a graph is considered as finite, undirected, with single lines and no loops. The arboricity of a graph G, denoted by Y(G), is the least number of line-disjoint spanning forests into which G can be partitioned. {x} is the least integer not less than X, and A(G) is the maximum degree among the points of G. V(G), E(G), and ISI denote the point set of G, the line set of G, and the number of elements of a set S!, respectively. L(G), M(G) and T(G) denote the line graph of G, the middle graph of G (see [3]), and the total graph of G respectively. Other definitions no* presented here may be found in [4]. Later on, the following two Theorems will be applied.