Root cube mean cordial labeling of Cn ? Cm, for n, m ? N

Abstract

All the graphs considered in this article 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) = bq((f(u))3+(f(v))3/2c 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 bxc denotes the greatest integer less than or equals to x. A Graph G is called root cube mean cordial if it admits root cube mean cordial labeling. In this article we have shown that the join of two cycles Cn ? Cm is not a root cube mean cordial and also we have provided graph which is root cube mean cordial.