One Modulo Three Harmonic Mean Labeling of some cycle-related graphs

Abstract

Let G=(V,E) be a graph with p vertices and q edges.

A function f :V(G)→{1,3,......,3q-2,3q} is called one modulo three harmonic mean labeling of G if f is injective and the induced function f* :E(G)→{1,4,......,3q-2} defined as 

f*(uv)=⌈2f(u)f(v)÷( f(u)+f(v))⌉ or ⌊2f(u)f(v)÷( f(u)+f(v))⌋ Ɐ u,v in E(G) is bijective.

A graph that admits  one modulo three harmonic meanlabeling is called one modulo three harmonic mean graph.

In this paper we prove 

T_nʘK_1, A( T_nʘK₁), M(P_n),  C_n^+t are one modulo three harmonic mean graph.