One Modulo Three Geometric Mean Graphs

A graph G is said to be one modulo three geometric mean graph if there is an injective function phi from the vertex set of G to the set {a mid 1leq a leq 3q-2} and either aequiv 0(mod 3) or aequiv 1(mod 3)} where q is the number of edges of G and phi induces a bijection phi^{*} form the edge set of G to {a mid 1leq aleq 3q-2 and aequiv 1(mod3)} given by phi^{*}(uv)=leftlceil sqrt{phi(u)phi(v)}rightrceil or leftlfloor sqrt{phi(u)phi(v)}rightrfloor and the function phi is called one modulo three geometric mean labeling of G. In this paper, we establish that some families of graphs admit one modulo three geometric mean labeling.the formula is not displayed correctly!