On the Generalized Complement of Some Graphs

A. In this paper we study the generalized complement of the graph G m,n = (V, E) for some values of m, n.We study the generalized complement of G m,n graphs with respect to the equal degree partition.The 2-complement of G m,n graphs are also determined for m = 2, n is even or odd.In particular, for some values of m, n ∈ N, we studied the complement of G m,n graphs with respect to the equal degree partition and the 2-complement of G m,n graphs.We determine the partitions P k , k ∈ N of the vertex set V such that the generalized complement of G m,n graph is a path graph and a comb graph.