Splitting digraphs

The problems related to the partitioning of undirected graphs using undirectional analogues with no loops and no multiple edges was studied. The problem regarding for which values d₁≥ d₂ ≥··· ≥ d_k 1, particularly finiteness of F(2,1) was analyzed. It was observed that the vertex set can be partitioned into two parts if the maximum degree is 2d+1. Characterization of all the sequences of integers (Δ, d₁, d₂, ·· ·, d_k) for the vertex set of any digraph showed that (m+n, ≥ q+r)digraph must contain either an (digraph, ≥q)-digraph, or an (n, ≥)-digraph to be (n, ≥ q)-digraph containing at least q outdegrees.