Heronian Mean Labeling of Dumbbell Graphs

Abstract

A graph  with  vertices and  edges is said to be a Heronian Mean graph if it is possible to label the vertices   with distinct labels  from  in such a way that when each

A graph  with  vertices and  edges is said to be a Heronian Mean graph if it is possible to label the vertices   with distinct labels  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 Heronian Mean labeling of  In this paper we prove that bicyclic related dumbbell graphs such as ,   and vertex-edge duplication  of are all heronian  mean graphs.

edge  is labeled with,

then the resulting edge labels are distinct. In this case   is called a Heronian Mean labeling of  In this paper we prove that bicyclic related dumbbell graphs such as ,   and vertex-edge duplication  of are all heronian  mean graphs.