Recognizing the Structure of Super Strongly Perfect Graphs Using Perfect Graphs and Strongly Perfect Graphs

A Graph G is Super Strongly Perfect Graph if every induced sub graphs H of G possesses a minimal dominating set that meets all the maximal complete sub graphs of H. We have given results about two important family members of Perfect graphs (i.e.,) Strongly Perfect Graphs and Super Strongly Perfect Graphs. We have discussed the structure of Super Strongly Perfect Graphs for Perfect Graphs like, Bipartite Graphs and Trees. We have also discussed the Super Strongly Perfect Graphs on Planar Graphs, Digraphs and 2 - Connected Graphs. We have found the relation between Strongly Perfect Graphs and Super Strongly Perfect Graphs.