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 edge  is labeled with  then the edge labels are distinct. In this case,  is called heronian mean labeling of  In this paper, we proved we prove that some new graphs such as Path union of two cycles ,  Path union of two cycles , Path union of two crowns  and  Path union of two crowns  all are heronian mean graphs.

Keywords: Graph, Heronian mean graph, Path, Cycle, Crown.

Mathematics subject classification: 05C78.