Let G = (V, E) be a graph with V = S1 S2 ...,St T where each Si is a set of vertices having at least two vertices and having the same degree and T = V Si. The degree splitting graph of G is denoted by DS(G) is obtained from G by adding vertices w1, w2, ..., wt and joining wi to each vertex of Si (1 i t). Let the vertices and the edges of a graph G are called the elements of G. In this...
