Logarithmic Mean Labeling of Duplicating a Vertex and an Edge of Some Graphs

Abstract

A function  is called a logarithmic mean labeling or  labeling of a graph  with  vertices and  edges if  is injective and the induced function  defined as

is bijective. A graph that admits a  labeling labeling is called a logarithmic mean graph or  graph. In this paper, we have discussed the logarithmic meanness of duplicating a vertex and an edge of some graphs.