  The distance of a vertex in a graph is the sum of distances from that vertex
to all other vertices of the graph. The Wiener index of a graph is the sum of
distances between all its unordered pairs of vertices. A graph has been
obtained that contains a vertex achieving the maximum distance among all graphs
on $n$ vertices with fixed number of cut vertices. Further the graphs having
maximum Wiener index among all graphs on $n$ vertices with at most $3$ cut
vertices have been characterised.
