A note on the minimum size of a vertex pancyclic graph

Let G be a graph on n greater than or equal to 3 vertices. Then G is vertex pancyclic if every vertex of G is contained in cycles of length 3,4,...,n. Let m(n) denote the minimum number of edges of a vertex pancyclic graph on n vertices. We show that m(3) = 3, m(4) = 5, m(5) = 7, m(6) = 9, and 3/2n < m(n) less than or equal to [5/3n](n greater than or equal to 7).