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A graph G=(V,E) with P vertices and q edges is called Lehmer-3 mean graph, if it is possible to label vertices x Є V with distinct label f(x) from 1,2,3,………….q+1 in such a way that when each edge e=uv is labeled with f(e=uv)=⌈ f(u) 3 +f(v) 3 f(u) 2 +f(v) 2 ⌉ (or) ⌊ f(u) 3 +f(v) 3 f(u) 2 +f(v) 2 ⌋, then the edge labels are distinct. In this case f is called Lehmer-3 mean labeling of G. In this paper we investigate Lehmer-3 mean labeling of some standard graphs.

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A Graph G = (V, E) with p vertices and q edges is called a harmonic mean graph if it is possible to label the vertices x ∈ V with distinct labels f (x) from 1, 2, . . . , q + 1 in such a way that when each edge e = uv is labeled with f (uv)