On the sum of the squares of all distances in bipartite graphs with given connectivity

Denote the sum of squares of all distances between all pairs of vertices in G by S(G). In this paper, sharp bounds on the S(G) are determined for several classes of connected bipartite graphs. All the extremal graphs having the minimal S(G) in the class of all connected n-vertex bipartite graphs with a given vertex connectivity (resp. edge-connectivity) can be identified.