A study on claw - Free graphs

The graphs G = [V(G), E(G)] consider in this article are finite of order |V(G)|= n, undirected, without loops and multiple edges. For any set A ⊂ V(G) denote by 〈A〉 the induced sub graph on A, G - A stands for [V(G)\A]. The words cycle and path mean elementary cycle or path. The vertex connectivity of G will be denoted by k(G), the circumference of G (i.e., the length of a longest cycle in G) by c(G), the girth of G (i.e., the length of a shortest cycle in G) by g(G) and the length of a longest path in G by p(G). By a clique mean a (not necessarily maximal) complete subgraph of G.