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All the graphs considered in this paper are simple and undirected. Let G = (V (G),E(G)) be a simple undirected graph. A function f : V (G) →{0, 1, 2} is called root cube mean cordial labeling if the induced function f∗ : E(G) →{0, 1, 2} defined by f∗(uv) = ⌊(f(u))3 +(f(v))3 2 ⌋ satisfies the condition |vf(i) − vf(j)|≤ 1 and |ef(i) − ef(j)|≤ 1 for any i,j ∈{0, 1, 2}, where vf(x) and ef(x) denotes the number of vertices and number of edges with label x, respectively, and ⌊x⌋ denotes the greatest integer less than or equals to x. The G is called root cube mean cordial if it admits root cube mean cordial labeling. In this paper, we have discussed root cube mean cordial labeling of some graphs. Also, we have provided some graphs which are not root cube mean cordial. [ABSTRACT FROM AUTHOR]