Root Square Mean Labeling of Theta Related Graphs

Abstract

A graph  with  vertices and  edges is called root square mean graph if it is possible to label the vertices   with distinct lables from  in such a way that when each edge  is labeled with 

  , then the resulting edge labels are distinct. In this case   is called a root square mean labeling of  In this paper we prove that theta related graphs such as are all root square mean graphs.