CHARACTERISATION OF VERY STRONGLY PERFECT GRAPHS

A graph G is said to be strongly perfect if every induced sub graph H has an independent set, meeting all maximal complete sub graphs of H. A strongly perfect graph is said to be very strongly perfect if it contains good independent set. It follows that every very strongly perfect graph is perfect not conversely. For example, the compliment of even cycle of length more than 4 is not very strongly perfect though it is perfect. In this paper, we characterise the classes of very strongly perfect graphs like cyclic graph, tadpole graph, barbell graph and friendship graph along with its independence number