Let G be a connected graph of order at least two.  We study about the monophonic sets and define a new set called the monophonic radius- distance monophonic set of a graph G. The monophonic radius was found for some corona related , path and cycle related graphs are found. Also Monophonic radius distance monophonic number are found.

Keywords: Monophonic distance,   distance monophonic set,  distance monophonic number

Mathematics Subject Classification 2010: 05C12.