Some realization results on edge monophonic number of a graph

For a connected graph g of order n,a set s of vertices is called an edge monophonic set of g if every edge of g lies on a monophonic path joining some pair of vertices in s,and the edge monophonic number me(g) is the minimum cardinality of an edge monophonic set. any edge monophonic set of cardinality me(g) is called a me-set of g. let m(g),g(g) and ge(g) denote the monophonic number,geodetic number and edge geodetic number,respectively of a graph. it is shown that for positive integers r,d,l and k with 2 ≤ r ≤ d ≤ 2r and 2 ≤ l ≤ k,there exists a connected graph g with radius r,diameter d,m(g) = l and me(g) = k. also,for integers a,b and c with 2 ≤ a ≤ b ≤ c,there exists a connected graph g such that (i) m(g) = a,me(g) = b and ge(g) = c; and (ii) m(g) = a,g(g) = b and ge(g) = c. © 2016,journal of prime research in mathematics.