ON THE STRENGTH OF CONNECTEDNESS OF A RANDOM GRAPH

If G is an arbitrary non-complete graph, let cp(G) denote the least number к such that by deleting к appropriately chosen vertices from G (i. e. deleting the к points in question and all edges starting from these points) the result­ ing graph is not connected. If G is a complete graph of order n, we put cv(G) = n — 1. Let ce(G) denote the least number / such that by deleting / appropriately chosen edges from G the resulting graph is not connected. We may measure the strength of connectedness of G by any of the numbers cP(G), c(G ) and in a certain sense (if G is known to be connected) also by c(G). Evidently one has