Let G be a graph with p-vertices and q edges. A graph G is said to be odd vertex even edge root square mean labelling if there exist an injective map f : V(G)→{1, 2, 3…..2q+1} such that the induced edge labels are even and distinct which can be obtained by f *(e) = √(f(u)2+f(v)2/2  or √f(u)2+f(v)2)/2. A graph that allows such labelling is called an odd vertex even edge root square mean labelling graph. This paper introduces this new labelling type and discusses several related theorems concerning path graphs.