The minimum number of edges in a vertex diameter-2-critical graph Original Research Article

A simple connected graph G with diam(G) = d is said to be ‘vertex diameter-d-critical’ if diam(G − x) ⩾ d + 1 for any x ∈ V(G). We prove that the number of edges in a vertex diameter-2-critical graph on n vertices with n ⩾ 23 is greater than or equal to (5n − 17)/2.