Edge Monophonic Domination Number of Graphs

In this paper the concept of edge monophonic domination num-ber of a graph is introduced.A set of vertices D of a graph G is edge mono-phonic domination set (EMD set) if it is both edge monophonic set and adomination set of G.The edge monophonic domination number (EMD num- ber) of G, me(G) is the cardinality of a minimum EMD set. EMD number of some connected graphs are realized.Connected graphs of order n with EMD number n are characterised.It is shown that for any two integers p and q such that 2 p q there exist a connected graph G with m(G) = p and me(G) = q.Also there is a connected graph G such that (G) = p;me(G) = q and me(G) = p + q