D- Complement and D(i)- Complement of a Graph.

A dominating set for a graph G = (V, E) is a subset D of V such that every point not in D is adjacent to at least one member of D. Let P = {P1, P2,. .., P k} be a partition of point set V (G). For all Pi and Pj in P of order k ≥ 2, i ̸ = j, delete the lines between Pi and Pj in G and include the lines between Pi and Pj which are not in G. The resultant graph thus obtained is k-complement of G with respect to the partition P and is denoted by G P k. For each set Vr in P of order k ≥ 1, delete the lines of G inside Vr and insert the lines of G joining the points of Vr. The graph G P k(i) thus obtained is called the k(i)-complement of G with respect to the partition P. In this paper, we define D-complement and D(i)-complement of a graph G. Further we study various properties of D and D(i) complements of a given graph. Index Terms-D-complement, D(i)-complement, γ-complement and γ(i)-complement. [ABSTRACT FROM AUTHOR]