GRAPHS WITH EXTREMAL CONNECTIVITY INDEX

Let G be a graph and -v the degree of its vertex v . The con- nectivity index of G is ´ = P (-u -v) i1=2 , with the summation ranging over all pairs of adjacent vertices of G. We oer a simple proof that (a) among n-vertex graphs without isolated vertices, the star has minimal ´- value, and (b) among n-vertex graphs, the graphs in which all components are regular of non-zero degree have maximal (mutually equal) ´-values. Both statements (a) and (b) are deduced using the same proof technique, based on linear programming.