Minimal graphs with prescribed vertex independence and clique numbers

The vertex independence number of a graph G is the maximal number of independent vertices in G. The clique number of G is the size of the largest complete subgraph of G. Let !1(v,n,r) denote the class of simple graphs on v vertices having vertex independence number n and clique number r. Let [(v,n,r) == min {dG): G E !1(v,n,r)}, where dG} denotes the number of edges in G, In this paper we study the class !1(v,n,r) and in particular, consider the problem of determining the function f( v, n, r ).