Modulo Three Harmonic Mean Labeling of Acyclic Graphs

Abstract

In this paper we give some definition and theorem of Modulo three harmonic mean labeling of graphs. A graph is said to be Modulo three harmonic mean labeling graph if there is a function ? from the vertex set of G {1,3,4,6,…, 3q-2, 3q} with ? is one to one and ? induces a bijective ?^* from the edge of G to {1,4,7, …, 3q-2} where ?^* (e= uv) ?(2?(u)?(v))/(?(u)+?(v)) ? or ? (2?(u)?(v))/(?(u)+?(v)) ? and the function ? is called as Modulo three mean labeling of G. Furthermore we define modulo three harmonic labeling of some trees.