Adding a Tail in Classes of Perfect Graphs

Consider a graph G which belongs to class C. We are interested in connecting node w∉V(G) by single edge uw where u∈V(G); we call such an tail. As the resulting from after addition of tail, denoted G+uw, need not belong C, want compute number non-edges minimum C-completion i.e., (excluding tail uw) be added G+uw so that In this paper, study problem for classes split, quasi-threshold, threshold and P4-sparse graphs present linear-time algorithms exploiting structure split tree representation graphs.