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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.
Dinesh Pandey (Sun,) studied this question.