COMPONENT ORDER EDGE CONNECTIVITY FOR GRAPHS OF FIXED SIZE AND ORDER

Given a graph G := (V, E) and an integer k >= 2, the component order edge connectivity of G is the smallest size of an edge set D such that the subgraph induced by G - D has all components of order less than k. Let G(n, m) denote the collection of simple graphs G which have n vertices and m edges. In this paper we consider properties of component order edge connectivity for G(n, m). Particularly we prove properties of the maximum and minimum values of the component order edge connectivity for G(n,m) for specific values of n, m and k.