Connected edge rm – distance monophonic number of a graph

Abstract

Let X be a graph of order at least two, which is connected. In this paper we define a new set called the connected edge rm - distance monophonic set of a graph X. Some properties of the connected edge rm -distance monophonic sets are determined. The parameter for connected edge rm - distance monophonic number is introduced. Many important results are determined and proved. Also, for every two integers a and b such that 2 ≤ a ≤ b, there exists a connected graph X with a as the edge rm -distance monophonic number and b as the connected edge rm -distance monophonic number of X is verified.