Graphs which have pancyclic complements

Let p and q denote the number of vertices and edges of a graph G, respectively. Let ”(G) denote the maximum degree of G, and G ˉ the complement of G. A graph G of order p is said to be pancyclic if G contains a cycle of each length n, 3 ￠ ‰ ¤n ￠ ‰ ¤p. For a nonnegative integer k, a connected graph G is said to be of rank k if q=p ￠ ’1+k. (For k equal to 0 and 1 these graphs are called trees and unicyclic graphs, respectively.)