THE MONOPHONIC DIAMETRAL PATH FIXING MONOPHONIC NUMBER OF A GRAPH

For a connected graph , let  be amonophonic diametral path of . A set  is called a monophonic set of  if every vertex of  lies on a  monophonic pathwhere and . The minimum cardinality of a  monophonic set of  is monophonic number of denoted by . A monophonic set of cardinality  is called a set ofG. monophonic number of  certain classes of graphs are studied. Connected graphs of order  with monophonic number  and  are characterized. It is shown that for integers with , there exists a connected graph  of order , with and .