Super Strongly Perfectness of Some Graphs

Abstract

A Graph G is Super Strongly Perfect Graph if every induced sub graph H of G possesses a minimal dominating set that meets all the maximal cliques of H. The structure of Super Strongly Perfect Graphs have been characterized by some classes of graphs like Cycle graphs, Circulant graphs, Complete graphs, Complete Bipartite graphs etc., In this paper, we have analysed some other graph classes like, Bicyclic graphs, Dumb bell graphs and Star graphs to characterize the structure of Super Strongly Perfect Graphs in a different way. By this we found the cardinality of minimal dominating set and maximal cliques of the above graphs.