Given an undirected multigraph G = (V;E) and a requirement function r : 0 V 2 1 ! Z + (where 0 V 2 1 is the set of all pairs of vertices and Z + is the set of nonnegative integers), we consider the problem of augmenting G by the smallest number of new edges so that the local edge-connectivity and vertex-connectivity b e t ween every pair x; y 2 V become at least r (x; y) and two, respectively. ...

The topic is the average order A(G) of a connected induced subgraph graph G. This generalizes, to graphs in general, subtree tree. In 1983 Jamison proved that order, over all trees n, minimized by path Pn, being A(Pn)=(n+2)/3. 2018, Kroeker, Mol, and Oellermann conjectured Pn minimizes G - conjecture was recently proved. this short note we show lower bound can be improved if connectivity known....